- published: 03 Nov 2014
- views: 2631
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In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
- published: 11 Jun 2015
- views: 1912
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
- published: 16 Jan 2012
- views: 15729
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same.
Teaching assistant: Liliana de Castro
Written & directed by Michael Harrison
Produced by Kimberly Hatch Harrison
Follow us on: http://google.com/+socratica
Also follow at: http://twitter.com/socratica
Learn more at: http://www.socratica.com
Subscribe at: http://www.youtube.com/subscription_center?add_user=SocraticaStudios
- published: 27 Feb 2015
- views: 25863
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism.
- published: 08 May 2011
- views: 11258
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group of integers under addition and the group of integers under addition.
- published: 03 Apr 2015
- views: 372
Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
Definition and notation
Given two groups (G, ∗) and (H, 
), a group isomorphism from (G, ∗) to (H, ) is a bijective group homomorphism from G to H. Spelled out, this means that a group isomorphism is a bijective function 
such that for all u and v in G it holds that
The two groups (G, ∗) and (H, ) are isomorphic if there exists an isomorphism from one to the other. This is written:
Often shorter and simpler notations can be used. When the relevant group operations are unambiguous they are omitted and one writes:
Sometimes one can even simply write G = H. Whether such a notation is possible without confusion or ambiguity depends on context. For example, the equals sign is not very suitable when the groups are both subgroups of the same group. See also the examples.
This page contains text from Wikipedia, the Free Encyclopedia -
http://wn.com/Group_isomorphism
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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5:11Group Theory 18: Definition of isomorphism
Group Theory 18: Definition of isomorphismGroup Theory 18: Definition of isomorphism
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23:30Group Isomorphisms Part 1
Group Isomorphisms Part 1Group Isomorphisms Part 1
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism. -
24:00GT9. Group Isomorphisms
GT9. Group IsomorphismsGT9. Group Isomorphisms
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html -
5:04Isomorphisms (Abstract Algebra)
Isomorphisms (Abstract Algebra)Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Teaching assistant: Liliana de Castro Written & directed by Michael Harrison Produced by Kimberly Hatch Harrison Follow us on: http://google.com/+socratica Also follow at: http://twitter.com/socratica Learn more at: http://www.socratica.com Subscribe at: http://www.youtube.com/subscription_center?add_user=SocraticaStudios -
14:30Group Isomorphism
Group IsomorphismGroup Isomorphism
Determine if two groups are isomorphic -
8:33Example of Group Isomorphism
Example of Group IsomorphismExample of Group Isomorphism
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism. -
7:13Binary Operations and Group Isomorphism
Binary Operations and Group Isomorphism -
20:29Group Theory 44, Group homomorphism, Isomorphism, examples
Group Theory 44, Group homomorphism, Isomorphism, examplesGroup Theory 44, Group homomorphism, Isomorphism, examples
Group Theory 44 -
11:53Proof: Group Isomorphism Integers Under Addition
Proof: Group Isomorphism Integers Under AdditionProof: Group Isomorphism Integers Under Addition
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group of integers under addition and the group of integers under addition. -
9:19Second Isomorphism Theorem for Groups Proof
Second Isomorphism Theorem for Groups Proof
-
Group Theory 18: Definition of isomorphism
-
Group Isomorphisms Part 1
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism. -
GT9. Group Isomorphisms
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html -
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Teaching assistant: Liliana de Castro Written & directed by Michael Harrison Produced by Kimberly Hatch Harrison Follow us on: http://google.com/+socratica Also follow at: http://twitter.com/socratica Learn more at: http://www.socratica.com Subscribe at: http://www.youtube.com/subscription_center?add_user=SocraticaStudios -
Group Isomorphism
Determine if two groups are isomorphic -
Example of Group Isomorphism
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism. -
-
Group Theory 44, Group homomorphism, Isomorphism, examples
Group Theory 44 -
Proof: Group Isomorphism Integers Under Addition
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group of integers under addition and the group of integers under addition. -
Group Theory 18: Definition of isomorphism
- Order: Reorder
- Duration: 5:11
- Updated: 03 Nov 2014
- views: 2631
- published: 03 Nov 2014
- views: 2631
Group Isomorphisms Part 1
- Order: Reorder
- Duration: 23:30
- Updated: 11 Jun 2015
- views: 1912
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
wn.com/Group Isomorphisms Part 1
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
- published: 11 Jun 2015
- views: 1912
GT9. Group Isomorphisms
- Order: Reorder
- Duration: 24:00
- Updated: 16 Jan 2012
- views: 15729
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for co...
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
wn.com/Gt9. Group Isomorphisms
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
- published: 16 Jan 2012
- views: 15729
Isomorphisms (Abstract Algebra)
- Order: Reorder
- Duration: 5:04
- Updated: 27 Feb 2015
- views: 25863
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are ...
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same.
Teaching assistant: Liliana de Castro
Written & directed by Michael Harrison
Produced by Kimberly Hatch Harrison
Follow us on: http://google.com/+socratica
Also follow at: http://twitter.com/socratica
Learn more at: http://www.socratica.com
Subscribe at: http://www.youtube.com/subscription_center?add_user=SocraticaStudios
wn.com/Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same.
Teaching assistant: Liliana de Castro
Written & directed by Michael Harrison
Produced by Kimberly Hatch Harrison
Follow us on: http://google.com/+socratica
Also follow at: http://twitter.com/socratica
Learn more at: http://www.socratica.com
Subscribe at: http://www.youtube.com/subscription_center?add_user=SocraticaStudios
- published: 27 Feb 2015
- views: 25863
Group Isomorphism
- Order: Reorder
- Duration: 14:30
- Updated: 14 May 2012
- views: 5812
Determine if two groups are isomorphic
Determine if two groups are isomorphic
wn.com/Group Isomorphism
Determine if two groups are isomorphic
- published: 14 May 2012
- views: 5812
Example of Group Isomorphism
- Order: Reorder
- Duration: 8:33
- Updated: 08 May 2011
- views: 11258
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of...
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism.
wn.com/Example Of Group Isomorphism
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism.
- published: 08 May 2011
- views: 11258
Binary Operations and Group Isomorphism
- Order: Reorder
- Duration: 7:13
- Updated: 15 Sep 2012
- views: 2858
How to construct a group binary operation based on existing group structure? This video describe a method to construct 'NEW' group from old using group isomorph...
How to construct a group binary operation based on existing group structure? This video describe a method to construct 'NEW' group from old using group isomorphism. This video make reference to John Fraleigh's Text
wn.com/Binary Operations And Group Isomorphism
Group Theory 44, Group homomorphism, Isomorphism, examples
- Order: Reorder
- Duration: 20:29
- Updated: 21 May 2013
- views: 6524
Group Theory 44
Group Theory 44
wn.com/Group Theory 44, Group Homomorphism, Isomorphism, Examples
Proof: Group Isomorphism Integers Under Addition
- Order: Reorder
- Duration: 11:53
- Updated: 03 Apr 2015
- views: 372
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group ...
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group of integers under addition and the group of integers under addition.
wn.com/Proof Group Isomorphism Integers Under Addition
Exploration of how to pick the appropriate mapping to establish a group isomorphism between groups concluding the the proof of an isomorphism between the group of integers under addition and the group of integers under addition.
- published: 03 Apr 2015
- views: 372
Second Isomorphism Theorem for Groups Proof
- Order: Reorder
- Duration: 9:19
- Updated: 01 Dec 2014
- views: 1648
Second Isomorphism Theorem for Groups Proof. If G is a group and H and K are subgroups of G, and K is normal in G, we prove that H/(H n K) is isomorphic to HK/K...
Second Isomorphism Theorem for Groups Proof. If G is a group and H and K are subgroups of G, and K is normal in G, we prove that H/(H n K) is isomorphic to HK/K.
wn.com/Second Isomorphism Theorem For Groups Proof
-
Graph isomorphism and automorphism group of a graph (MATH)
Subject :- Mathematics Paper:-Number Theory and Graph Theory Principal Investigator:- Prof.M.Majumdar -
The Kernel of a Group Homomorphism – Abstract Algebra
The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different homomorphisms between G and H can give different kernels. If f is an isomorphism, then the kernel will simply be the identity element. You can also define a kernel for a homomorphism between other objects in abstract algebra: rings, fields, vector spaces, modules. We will cover these in separate videos. ******** Subscribe today! http://www.youtube.com/subscription_center?add_user=SocraticaStudios Circle us on Google+ at http://google.com/+socratica Follow us on Twitter at https://twitter.com/socratica... -
Visual Group Theory, Lecture 4.5: The isomorphism theorems
Visual Group Theory, Lecture 4.5: The isomorphism theorems There are four central results in group theory that are collectively known at the isomorphism theorems. We introduced the first of these a few lectures back, under the name of the "fundamental homomorphism theorem." In this lecture, we will see the other three, and we will motivate each one visually. We will prove one of these, sketch the proof of another, and leave the last proof as an exercise. After that, we introduce the notion of a commutator, which corresponds to a "non-abelian fragment" of a Cayley diagram. The commutators generate a normal subgroups, whose quotient yields an abelian group. We state this as a universal property, and close with a few examples. Course webpage (with lecture notes, HW, etc.): http://www.math.c... -
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagrams before formally stating and proving it. This gives us a 2nd way to prove that two groups are isomorphic, which is often easier than constructing an explicit isomorphism. We conclude by applying the FHT to construct cyclic groups as natural quotients of the integers. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html -
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html -
Graph isomorphism in quasipolynomial time II - László Babai
Computer Science/Discrete Mathematics Seminar II Topic:Graph isomorphism in quasipolynomial time II Speaker: László Babai Date:Tuesday, March 1 The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be ... -
Graph isomorphism in quasipolynomial time - László Babai
Computer Science/Discrete Mathematics Seminar I Topic: Graph isomorphism in quasipolynomial time I Speaker: László Babai Date: Monday, February 29 The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will ... -
Group isomorphism
Group isomorphism In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.If there exists an isomorphism between two groups, then the groups are called isomorphic. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=S-YHiZAYVkU -
Group Isomorphism: explanation and practical application
Describes group isomorphisms and gives an historically significant example. NOTE: at 2:14 I say "even times odd is odd" but should have said "even plus odd is odd" -
Group homomorphisms and isomorphisms
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can help you tell a lot about the properties of groups.
Graph isomorphism and automorphism group of a graph (MATH)
- Order: Reorder
- Duration: 31:01
- Updated: 19 May 2016
- views: 22
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
wn.com/Graph Isomorphism And Automorphism Group Of A Graph (Math)
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
- published: 19 May 2016
- views: 22
The Kernel of a Group Homomorphism – Abstract Algebra
- Order: Reorder
- Duration: 4:53
- Updated: 03 May 2016
- views: 4087
The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel...
The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different homomorphisms between G and H can give different kernels.
If f is an isomorphism, then the kernel will simply be the identity element.
You can also define a kernel for a homomorphism between other objects in abstract algebra: rings, fields, vector spaces, modules. We will cover these in separate videos.
********
Subscribe today! http://www.youtube.com/subscription_center?add_user=SocraticaStudios
Circle us on Google+ at http://google.com/+socratica
Follow us on Twitter at https://twitter.com/socratica
Like us on Facebook at https://www.facebook.com/SocraticaStudios
********
Teaching assistant: Liliana de Castro
Written & directed by Michael Harrison
Produced by Kimberly Hatch Harrison
wn.com/The Kernel Of A Group Homomorphism – Abstract Algebra
The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different homomorphisms between G and H can give different kernels.
If f is an isomorphism, then the kernel will simply be the identity element.
You can also define a kernel for a homomorphism between other objects in abstract algebra: rings, fields, vector spaces, modules. We will cover these in separate videos.
********
Subscribe today! http://www.youtube.com/subscription_center?add_user=SocraticaStudios
Circle us on Google+ at http://google.com/+socratica
Follow us on Twitter at https://twitter.com/socratica
Like us on Facebook at https://www.facebook.com/SocraticaStudios
********
Teaching assistant: Liliana de Castro
Written & directed by Michael Harrison
Produced by Kimberly Hatch Harrison
- published: 03 May 2016
- views: 4087
Visual Group Theory, Lecture 4.5: The isomorphism theorems
- Order: Reorder
- Duration: 46:19
- Updated: 23 Mar 2016
- views: 151
Visual Group Theory, Lecture 4.5: The isomorphism theorems
There are four central results in group theory that are collectively known at the isomorphism theore...
Visual Group Theory, Lecture 4.5: The isomorphism theorems
There are four central results in group theory that are collectively known at the isomorphism theorems. We introduced the first of these a few lectures back, under the name of the "fundamental homomorphism theorem." In this lecture, we will see the other three, and we will motivate each one visually. We will prove one of these, sketch the proof of another, and leave the last proof as an exercise. After that, we introduce the notion of a commutator, which corresponds to a "non-abelian fragment" of a Cayley diagram. The commutators generate a normal subgroups, whose quotient yields an abelian group. We state this as a universal property, and close with a few examples.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
wn.com/Visual Group Theory, Lecture 4.5 The Isomorphism Theorems
Visual Group Theory, Lecture 4.5: The isomorphism theorems
There are four central results in group theory that are collectively known at the isomorphism theorems. We introduced the first of these a few lectures back, under the name of the "fundamental homomorphism theorem." In this lecture, we will see the other three, and we will motivate each one visually. We will prove one of these, sketch the proof of another, and leave the last proof as an exercise. After that, we introduce the notion of a commutator, which corresponds to a "non-abelian fragment" of a Cayley diagram. The commutators generate a normal subgroups, whose quotient yields an abelian group. We state this as a universal property, and close with a few examples.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
- published: 23 Mar 2016
- views: 151
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
- Order: Reorder
- Duration: 32:52
- Updated: 20 Mar 2016
- views: 189
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem",...
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagrams before formally stating and proving it. This gives us a 2nd way to prove that two groups are isomorphic, which is often easier than constructing an explicit isomorphism. We conclude by applying the FHT to construct cyclic groups as natural quotients of the integers.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
wn.com/Visual Group Theory, Lecture 4.3 The Fundamental Homomorphism Theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagrams before formally stating and proving it. This gives us a 2nd way to prove that two groups are isomorphic, which is often easier than constructing an explicit isomorphism. We conclude by applying the FHT to construct cyclic groups as natural quotients of the integers.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
- published: 20 Mar 2016
- views: 189
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
- Order: Reorder
- Duration: 47:18
- Updated: 18 Mar 2016
- views: 184
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds fo...
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
wn.com/Visual Group Theory, Lecture 4.1 Homomorphisms And Isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
- published: 18 Mar 2016
- views: 184
Graph isomorphism in quasipolynomial time II - László Babai
- Order: Reorder
- Duration: 68:25
- Updated: 01 Mar 2016
- views: 202
Computer Science/Discrete Mathematics Seminar II
Topic:Graph isomorphism in quasipolynomial time II
Speaker: László Babai
Date:Tuesday, March 1
The algorithm i...
Computer Science/Discrete Mathematics Seminar II
Topic:Graph isomorphism in quasipolynomial time II
Speaker: László Babai
Date:Tuesday, March 1
The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be assumed. The paper is available at arXiv:1512.03547. Helpful reading: Eugene M. Luks: Isomorphism of graphs of bounded valence can be tested in polynomial time. JCSS 25(1) (1982) 42--65.
For more videos, visit http://video.ias.edu
wn.com/Graph Isomorphism In Quasipolynomial Time Ii László Babai
Computer Science/Discrete Mathematics Seminar II
Topic:Graph isomorphism in quasipolynomial time II
Speaker: László Babai
Date:Tuesday, March 1
The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be assumed. The paper is available at arXiv:1512.03547. Helpful reading: Eugene M. Luks: Isomorphism of graphs of bounded valence can be tested in polynomial time. JCSS 25(1) (1982) 42--65.
For more videos, visit http://video.ias.edu
- published: 01 Mar 2016
- views: 202
Graph isomorphism in quasipolynomial time - László Babai
- Order: Reorder
- Duration: 89:57
- Updated: 29 Feb 2016
- views: 515
Computer Science/Discrete Mathematics Seminar I
Topic: Graph isomorphism in quasipolynomial time I
Speaker: László Babai
Date: Monday, February 29
The algorith...
Computer Science/Discrete Mathematics Seminar I
Topic: Graph isomorphism in quasipolynomial time I
Speaker: László Babai
Date: Monday, February 29
The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be assumed. The paper is available at arXiv:1512.03547. Helpful reading: Eugene M. Luks: Isomorphism of graphs of bounded valence can be tested in polynomial time. JCSS 25(1) (1982) 42--65.
For more videos, visit http://video.ias.edu
wn.com/Graph Isomorphism In Quasipolynomial Time László Babai
Computer Science/Discrete Mathematics Seminar I
Topic: Graph isomorphism in quasipolynomial time I
Speaker: László Babai
Date: Monday, February 29
The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of the technical details will be given in the second talk, with a focus on the core group theoretic routine ("Local Certificates") and the aggregation of the the local certificates. Time permitting, we also discuss one of the combinatorial partitioning algorithms ("Design lemma"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be assumed. The paper is available at arXiv:1512.03547. Helpful reading: Eugene M. Luks: Isomorphism of graphs of bounded valence can be tested in polynomial time. JCSS 25(1) (1982) 42--65.
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- published: 29 Feb 2016
- views: 515
Group isomorphism
- Order: Reorder
- Duration: 8:28
- Updated: 22 Jan 2016
- views: 10
Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of ...
Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.If there exists an isomorphism between two groups, then the groups are called isomorphic.
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wn.com/Group Isomorphism
Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.If there exists an isomorphism between two groups, then the groups are called isomorphic.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=S-YHiZAYVkU
- published: 22 Jan 2016
- views: 10
Group Isomorphism: explanation and practical application
- Order: Reorder
- Duration: 11:39
- Updated: 27 Nov 2015
- views: 28
Describes group isomorphisms and gives an historically significant example.
NOTE: at 2:14 I say "even times odd is odd" but should have said "even plus odd is o...
Describes group isomorphisms and gives an historically significant example.
NOTE: at 2:14 I say "even times odd is odd" but should have said "even plus odd is odd"
wn.com/Group Isomorphism Explanation And Practical Application
Describes group isomorphisms and gives an historically significant example.
NOTE: at 2:14 I say "even times odd is odd" but should have said "even plus odd is odd"
- published: 27 Nov 2015
- views: 28
Group homomorphisms and isomorphisms
- Order: Reorder
- Duration: 14:53
- Updated: 17 Nov 2015
- views: 356
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can help you tell a lot about the properties of groups.
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can help you tell a lot about the properties of groups.
wn.com/Group Homomorphisms And Isomorphisms
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can help you tell a lot about the properties of groups.
- published: 17 Nov 2015
- views: 356
-
Group Isomorphisms Part 2
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism. -
Group Isomorphism and Hypergraph Isomorphism
Speaker: Dr. Paolo Codenotti Title: Group Isomorphism and Hypergraph Isomorphism Abstract: I will talk about connections between group theory and combinatorics that arise in isomorphism testing. Our main results are algorithms to test isomorphism of hypergraphs and of groups. We will highlight the ways in which both combinatorial and group theoretic techniques can be used in these contexts. -
Modern Algebra (Abstract Algebra) Made Easy - Part 8 - Group Homomorphisms
http://www.pensieve.net/course/13 In this video, I give definitions, examples, and proofs talking about group homomorphisms. Hope you like it. Feel free to give me some constructive feedback! Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words. -
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
Group Isomorphisms Part 2
- Order: Reorder
- Duration: 33:05
- Updated: 11 Jun 2015
- views: 1168
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
wn.com/Group Isomorphisms Part 2
In this video we discuss the concept of two groups being isomorphic and of a group isomorphism.
- published: 11 Jun 2015
- views: 1168
Group Isomorphism and Hypergraph Isomorphism
- Order: Reorder
- Duration: 54:44
- Updated: 18 Feb 2012
- views: 1185
Speaker: Dr. Paolo Codenotti
Title: Group Isomorphism and Hypergraph Isomorphism
Abstract: I will talk about connections between group theory and combinator...
Speaker: Dr. Paolo Codenotti
Title: Group Isomorphism and Hypergraph Isomorphism
Abstract: I will talk about connections between group theory and combinatorics
that arise in isomorphism testing. Our main results are algorithms to
test isomorphism of hypergraphs and of groups. We will highlight the
ways in which both combinatorial and group theoretic techniques can be
used in these contexts.
wn.com/Group Isomorphism And Hypergraph Isomorphism
Speaker: Dr. Paolo Codenotti
Title: Group Isomorphism and Hypergraph Isomorphism
Abstract: I will talk about connections between group theory and combinatorics
that arise in isomorphism testing. Our main results are algorithms to
test isomorphism of hypergraphs and of groups. We will highlight the
ways in which both combinatorial and group theoretic techniques can be
used in these contexts.
- published: 18 Feb 2012
- views: 1185
Modern Algebra (Abstract Algebra) Made Easy - Part 8 - Group Homomorphisms
- Order: Reorder
- Duration: 33:09
- Updated: 21 Nov 2012
- views: 19781
http://www.pensieve.net/course/13
In this video, I give definitions, examples, and proofs talking about group homomorphisms. Hope you like it. Feel free to giv...
http://www.pensieve.net/course/13
In this video, I give definitions, examples, and proofs talking about group homomorphisms. Hope you like it. Feel free to give me some constructive feedback!
Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words.
wn.com/Modern Algebra (Abstract Algebra) Made Easy Part 8 Group Homomorphisms
http://www.pensieve.net/course/13
In this video, I give definitions, examples, and proofs talking about group homomorphisms. Hope you like it. Feel free to give me some constructive feedback!
Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words.
- published: 21 Nov 2012
- views: 19781
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
- Order: Reorder
- Duration: 32:02
- Updated: 19 Aug 2012
- views: 10008
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n...
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
wn.com/Algtopreview3 More On Commutative Groups Isomorphisms, Homomorphisms, Cosets And Quotient Groups
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
- published: 19 Aug 2012
- views: 10008
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5:11
Group Theory 18: Definition of isomorphism
published: 03 Nov 2014
Group Theory 18: Definition of isomorphism
Group Theory 18: Definition of isomorphism
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- published: 03 Nov 2014
- views: 2631
23:30
Group Isomorphisms Part 1
In this video we discuss the concept of two groups being isomorphic and of a group isomorp...
published: 11 Jun 2015
Group Isomorphisms Part 1
Group Isomorphisms Part 1
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- published: 11 Jun 2015
- views: 1912
24:00
GT9. Group Isomorphisms
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups....
published: 16 Jan 2012
GT9. Group Isomorphisms
GT9. Group Isomorphisms
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- published: 16 Jan 2012
- views: 15729
5:04
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism bet...
published: 27 Feb 2015
Isomorphisms (Abstract Algebra)
Isomorphisms (Abstract Algebra)
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- published: 27 Feb 2015
- views: 25863
14:30
Group Isomorphism
Determine if two groups are isomorphic
published: 14 May 2012
Group Isomorphism
Group Isomorphism
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- published: 14 May 2012
- views: 5812
8:33
Example of Group Isomorphism
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that...
published: 08 May 2011
Example of Group Isomorphism
Example of Group Isomorphism
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- published: 08 May 2011
- views: 11258
7:13
Binary Operations and Group Isomorphism
How to construct a group binary operation based on existing group structure? This video de...
published: 15 Sep 2012
Binary Operations and Group Isomorphism
Binary Operations and Group Isomorphism
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- published: 15 Sep 2012
- views: 2858
20:29
Group Theory 44, Group homomorphism, Isomorphism, examples
Group Theory 44
published: 21 May 2013
Group Theory 44, Group homomorphism, Isomorphism, examples
Group Theory 44, Group homomorphism, Isomorphism, examples
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- published: 21 May 2013
- views: 6524
11:53
Proof: Group Isomorphism Integers Under Addition
Exploration of how to pick the appropriate mapping to establish a group isomorphism betwee...
published: 03 Apr 2015
Proof: Group Isomorphism Integers Under Addition
Proof: Group Isomorphism Integers Under Addition
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- published: 03 Apr 2015
- views: 372
9:19
Second Isomorphism Theorem for Groups Proof
Second Isomorphism Theorem for Groups Proof. If G is a group and H and K are subgroups of ...
published: 01 Dec 2014
Second Isomorphism Theorem for Groups Proof
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31:01
Graph isomorphism and automorphism group of a graph (MATH)
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof...
published: 19 May 2016
Graph isomorphism and automorphism group of a graph (MATH)
Graph isomorphism and automorphism group of a graph (MATH)
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- published: 19 May 2016
- views: 22
4:53
The Kernel of a Group Homomorphism – Abstract Algebra
The kernel of a group homomorphism measures how far off it is from being one-to-one (an in...
published: 03 May 2016
The Kernel of a Group Homomorphism – Abstract Algebra
The Kernel of a Group Homomorphism – Abstract Algebra
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- published: 03 May 2016
- views: 4087
46:19
Visual Group Theory, Lecture 4.5: The isomorphism theorems
Visual Group Theory, Lecture 4.5: The isomorphism theorems
There are four central results...
published: 23 Mar 2016
Visual Group Theory, Lecture 4.5: The isomorphism theorems
Visual Group Theory, Lecture 4.5: The isomorphism theorems
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- published: 23 Mar 2016
- views: 151
32:52
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
The fundamental ho...
published: 20 Mar 2016
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
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- published: 20 Mar 2016
- views: 189
47:18
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is functi...
published: 18 Mar 2016
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
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- published: 18 Mar 2016
- views: 184
68:25
Graph isomorphism in quasipolynomial time II - László Babai
Computer Science/Discrete Mathematics Seminar II
Topic:Graph isomorphism in quasipolynomia...
published: 01 Mar 2016
Graph isomorphism in quasipolynomial time II - László Babai
Graph isomorphism in quasipolynomial time II - László Babai
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- published: 01 Mar 2016
- views: 202
89:57
Graph isomorphism in quasipolynomial time - László Babai
Computer Science/Discrete Mathematics Seminar I
Topic: Graph isomorphism in quasipolynomia...
published: 29 Feb 2016
Graph isomorphism in quasipolynomial time - László Babai
Graph isomorphism in quasipolynomial time - László Babai
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- published: 29 Feb 2016
- views: 515
8:28
Group isomorphism
Group isomorphism
In abstract algebra, a group isomorphism is a function between two gr...
published: 22 Jan 2016
Group isomorphism
Group isomorphism
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- published: 22 Jan 2016
- views: 10
11:39
Group Isomorphism: explanation and practical application
Describes group isomorphisms and gives an historically significant example.
NOTE: at 2:14 ...
published: 27 Nov 2015
Group Isomorphism: explanation and practical application
Group Isomorphism: explanation and practical application
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- published: 27 Nov 2015
- views: 28
14:53
Group homomorphisms and isomorphisms
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can h...
published: 17 Nov 2015
Group homomorphisms and isomorphisms
Group homomorphisms and isomorphisms
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- published: 17 Nov 2015
- views: 356
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33:05
Group Isomorphisms Part 2
In this video we discuss the concept of two groups being isomorphic and of a group isomorp...
published: 11 Jun 2015
Group Isomorphisms Part 2
Group Isomorphisms Part 2
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- published: 11 Jun 2015
- views: 1168
54:44
Group Isomorphism and Hypergraph Isomorphism
Speaker: Dr. Paolo Codenotti
Title: Group Isomorphism and Hypergraph Isomorphism
Abstra...
published: 18 Feb 2012
Group Isomorphism and Hypergraph Isomorphism
Group Isomorphism and Hypergraph Isomorphism
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- published: 18 Feb 2012
- views: 1185
33:09
Modern Algebra (Abstract Algebra) Made Easy - Part 8 - Group Homomorphisms
http://www.pensieve.net/course/13
In this video, I give definitions, examples, and proofs...
published: 21 Nov 2012
Modern Algebra (Abstract Algebra) Made Easy - Part 8 - Group Homomorphisms
Modern Algebra (Abstract Algebra) Made Easy - Part 8 - Group Homomorphisms
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- published: 21 Nov 2012
- views: 19781
32:02
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
We present more information on commutative groups and the fundamental structure theorem th...
published: 19 Aug 2012
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
- Report rights infringement
- published: 19 Aug 2012
- views: 10008
Group Isomorphisms Part 2...
Group Isomorphism and Hypergraph Isomorphism...
Modern Algebra (Abstract Algebra) Made Easy - Part...
AlgTopReview3: More on commutative groups---isomor...
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Turkish Military in Attempted Coup, Prime Minister Says
Edit Bloomberg 15 Jul 2016
Ankara, Turkey (AP) -- Turkey's prime minister says a group within Turkey's military has engaged in what ......
photo: AP / Emrah Gurel
Live: Turkish army says it has taken power in the country
Edit France24 15 Jul 2016photo: AP / Carolyn Kaster
Former Fox News Commentator Sentenced For False Claims Of CIA Ties
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U.S ... District Court in Alexandria, Virginia, the U.S. Attorney's Office said in a statement.Dana Boente, U.S. Attorney for the Eastern District of Virginia, issued to the statement."Wayne Simmons is a fraud ... - Dana BoenteU.S. District Judge T.S....
photo: FEMA / Bill Koplitz
Newly Released Pages Say Saudis May Have Helped 9/11 Attackers
Edit WorldNews.com 15 Jul 2016
Saudi nationals connected to the government in Riyadh may have aided some of the Sept. 11 hijackers in the U.S ... intelligence officials who approved releasing the report, as families of some of the 3,000 victims of the attacks have long demanded, emphasized that they didn’t consider it accurate or reliable ... WN.com, Jim Berrie ....
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Nice Terrorist Attack: At Least 77 Dead, Police Kill Suspect
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Images broadcast from the attack on French media showed the gruesome scene with massive groups of people fleeing for their lives down the palm tree-lined Promenade des Anglais, Eric Ciotti said on BFM TV how police killed the driver after an exchange of gunfire after a man started shooting upon exiting the truck ... groups including the Islamic State....
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Zone Group II - Friday (Davis Cup)
Edit Public Technologies 16 Jul 2016
Lithuania and Belarus among nations to take 2-0 lead after Friday as potential promotion play-off ties become clearer across Zone Group II. Europe/Africa Zone Group II. Lithuania and Belarus made perfect starts to their second round ties in Europe/Africa Zone Group II as they earned 2-0 leads over South Africa and Latvia respectively ... Asia/Oceania Zone Group II ... The loser of each tie will drop down to Zone Group III in 2017....
Pre-close Trading Update (K3 Business Technology Group plc)
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K3 Business Technology Group plc) ... K3 Business Technology Group. ('K3' or 'the Group') ... The Group's overall trading performance remains encouraging, particularly in core sectors, and results for the full year are expected to be broadly in line with market expectations, notwithstanding the impact of a major customer entering administration in June ... Group plc....
Financial highlights (Management Consulting Group plc)
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Management Consulting Group plc) ... The reported results for 2015 from the Group's continuing operations, being the Kurt Salmon business which the Group has retained together with Alexander Proudfoot, are in line with the trading update provided at the time of the Circular sent to shareholders dated 30 November 2015 ... continuing operations of the Group....
Members of the Iraqi armed forces march during a military parade at...
Edit Topix 16 Jul 2016
... march during a military parade at Tahrir Square in central Baghdad to celebrate the recapture of Fallujah from the Islamic State group jihadists....
Caregiver support group at ELMONT PUBLIC LIBRARY - August,2016 (Nassau County, NY)
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Mangano announced today that the County Offices for Aging and Mental Health, in cooperation with the Elmont Public Library, are offering a support group specifically targeted to respond to the needs of elder caregivers ... The group is led by Marguerite Dilimetin, LCSW, CASAC, Support Group Facilitator....
OEG sold a subsidiary that owns the Hilton hotel complex building in Estonia
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OEG group company Jessy Investments B.V. entered into an agreement to divest the 100% holding in its Estonian subsidiary Kesklinna Hotelli OAoe that owns the hotel and entertainment complex building in Tallinn, where the Hilton Tallinn Park hotel and the flagship casino of OEG group, Olympic Park Casino, are based in. The buyer is East Capital group company ECB3 Tallinn OAoe ... ....
AFG strengthens their Building Technology Division’s portfolio with the acquisition of the Koralle Group (Baker & McKenzie LLP)
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Leading Global law firm Baker & McKenzie has provided legal assistance to Arbonia-Forster-Holding (AFG) with its acquisition of the Koralle Group, a company specializing in sanitary facilities, from Geberit AG ... The Koralle Group was taken over by Geberit AG as part of the Sanitec acquisition in 2015 ... The existing brands of the Koralle Group will continue to be traded independently on the market....
Zone Group I - Friday (Davis Cup)
Edit Public Technologies 16 Jul 2016
(Source. Davis Cup). Spain open up a 2-0 lead against Romania while China and Uzbekistan end the day level as teams compete to make the World Group play-offs. Europe/Africa Zone Group I. All four of the second round ties finished the opening day with a 2-0 score line as Spain, Russia, Slovakia and Ukraine all within a single victory of progressing to the World Group play-offs in September ... Asia/Oceania Zone Group I ... Americas Zone Group I....
Italy's plan to legalize weed could fight both the Islamic State and the mafia
Edit Business Insider 16 Jul 2016
Sirte, a city in Libya along that route, has been under IS' control since February 2015, though anti-IS rebels are now attempting to regain control of the group's last stronghold in the country ... Roberti's call to legalize marijuana comes as law enforcement agencies in Italy have begun to view the fight against terror and organized crime as one and the same, with once separate strategies to fight the groups converging....
Rosters confirmed on the eve of FIBA U20 European Championship (FIBA Asia)
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(Source. FIBA Asia). HELSINKI, Finland (FIBA U20 European Championship 2016) - The finalised rosters of the 16 participating teams at the FIBA U20 European Championship 2016 have been verified and confirmed ... Group A. Turkey, Hungary, Germany, Lithuania Group B. Spain, Israel, Finland, France Group C. Serbia, Slovenia, Ukraine, Latvia Group D. Italy, Sweden, Belgium, Czech Republic ... ###. About FIBA ... (noodl....
'Smoke-in' protesters just wanted to be heard
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Multiple sclerosis sufferer Justin Loizos led a group of frustrated medical marijuana patients into a downtown intersection on Friday for a smoke session which shut down traffic. The group of about 30 protesters were diverse but united in their mission to be heard ... were protesting Bill 178 which groups medical marijuana in with tobacco products in the Ontario Smoke Free Act....
US using Daesh as repression tool against Mideast countries: Analyst
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The United States government is using the Daesh (ISIL) Takfiri terrorist group as a repression tool against various governments in the Middle East, says an American political analyst ... The general’s comments came just three days after US President Barack Obama's administration announced a 560 troop increase to allegedly fight the Daesh terror group in Iraq and Syria....
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