Index of a subgroup

In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively "half" of the elements of G lie in H. The index of H in G is usually denoted |G : H| or [G : H] or (G:H).

Formally, the index of H in G is defined as the number of cosets of H in G. (The number of left cosets of H in G is always equal to the number of right cosets.) For example, let Z be the group of integers under addition, and let 2Z be the subgroup of Z consisting of the even integers. Then 2Z has two cosets in Z (namely the even integers and the odd integers), so the index of 2Z in Z is two. To generalize,

for any positive integer n.

If N is a normal subgroup of G, then the index of N in G is also equal to the order of the quotient group G / N, since this is defined in terms of a group structure on the set of cosets of N in G.

If G is infinite, the index of a subgroup H will in general be a non-zero cardinal number. It may be finite - that is, a positive integer - as the example above shows.

Remix (book)

Remix: Making Art and Commerce Thrive in the Hybrid Economy is Lawrence Lessig's fifth book. It is available as a free download under a Creative Commons license. It details a hypothesis about the societal effect of the Internet, and how this will affect production and consumption of popular culture.

Summary

In Remix Lawrence Lessig, a Harvard law professor and a respected voice in what he deems the "copyright wars", describes the disjuncture between the availability and relative simplicity of remix technologies and copyright law. Lessig insists that copyright law as it stands now is antiquated for digital media since every "time you use a creative work in a digital context, the technology is making a copy" (98). Thus, amateur use and appropriation of digital technology is under unprecedented control that previously extended only to professional use.

Lessig insists that knowledge and manipulation of multi-media technologies is the current generation's form of "literacy"- what reading and writing was to the previous. It is the vernacular of today. The children growing up in a world where these technologies permeate their daily life are unable to comprehend why "remixing" is illegal. Lessig insists that amateur appropriation in the digital age cannot be stopped but only 'criminalized'. Thus most corrosive outcome of this tension is that generations of children are growing up doing what they know is "illegal" and that notion has societal implications that extend far beyond copyright wars. The book is now available as a free download under one of the Creative Commons' licenses.

Remix'5

Remix'5 is a Candan Erçetin album. It was remixes of Melek. There's also a song from "Les Choristes" movie, 'Sevdim Anladım'.

Track listing

Cypher (album)

Cypher is the fourth album by industrial black metal band ...And Oceans. The original name of the album was set to be Insect Angels and Devil Worms, but was changed.

Track listing

Credits

Cypher (film)

Cypher (also known as Brainstorm), is a 2002 science fiction thriller film starring Jeremy Northam and Lucy Liu. It was written by Brian King and directed by Vincenzo Natali. Jeremy Northam plays an accountant whose hope for a career in corporate espionage takes an unexpected turn. The film was shown in limited release in theaters in the US and Australia, and released on DVD on August 2, 2005. The film received mixed reviews, and Northam received the Best Actor award at the Sitges Film Festival.

Plot

Morgan Sullivan (Northam), a recently unemployed accountant, is bored with his suburban life. Pressured by his wife to take a job with her father's company, he instead pursues a position in corporate espionage. Digicorp's Head of Security, Finster (Bennett), inducts Morgan and assigns him a new identity. As Jack Thursby, he is sent to conventions to secretly record presentations and transmit them to headquarters. Sullivan is soon haunted by recurring nightmares and neck pain. When he meets Rita Foster (Liu) from a competing corporation, his life starts to become complicated.

Omen (Soulfly album)

Omen is the seventh studio album from the metal band Soulfly. It was recorded in November 2009 and was released first in Japan on May 18, 2010 and on May 25, 2010 in other parts of the world. It was released on May 24, 2010 in parts of Europe. It is the last album to feature bassist Bobby Burns and drummer Joe Nunez who were replaced by Asesino frontman, Tony Campos and former Borknagar drummer David Kinkade in mid-2011. At just over forty and a half minutes, it was the band's shortest album until Archangel was released five years later, which ran for thirty-six and a half minutes.

Background

Soulfly entered the Edge of the Earth Studios in Los Angeles, California on November 6, 2009 to begin recording their seventh album with Max Cavalera and Logan Mader both producing. Through a series of streaming web video updates, frontman Max Cavalera revealed on November 13, 2009 that the album would be called Omen and would feature guest appearances by Tommy Victor of Prong and Greg Puciato of The Dillinger Escape Plan. Additionally, the album features performances on drums from Max's first son Zyon Cavalera on a b-side cover of Sepultura's "Refuse-Resist" and his youngest son Igor Cavalera on a cover of Excel's "Your Life, My Life".

Omen (rapper)

Omen, is an American rapper and producer from Chicago, Illinois. He is signed to J. Cole's Dreamville Records and Interscope Records. His debut studio album Elephant Eyes, was released on July 21, 2015.

Musical career

2010-2013

In 2010, Omen released his first mixtape, Delayed. The following year, he released critically acclaimed mixtape, Afraid of Heights. The mixtape includes guest features from J. Cole and Kendrick Lamar, among others.

2014-present

In 2014, Omen then appeared on the Dreamville compilation mixtape Revenge of the Dreamers. That mixtape was released in celebration of Dreamville's partnership with Interscope Records.

On July 21, 2015, Omen's debut album, Elephant Eyes, was released after a few setbacks and date changes. During the Spring and Summer of 2015 Omen, was a part of the J.Cole's "2014 Forest Hills Drive" Tour with other acts Bas, Cozz, Pusha T, Jhene Aiko, Jeremih, YG, Big Sean, which brought him across North America as well as Europe. In the Fall of 2015 he will go on his own Elephant Eyes Tour hitting Los Angeles, as well as, Boston, New York and his Hometown Chicago.