In abstract algebra, the symmetry group of an object (image, signal, etc.) is the group of all isometries under which the object is invariant with composition as the operation. It is a subgroup of the isometry group of the space concerned. If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts; see below.

The "objects" may be geometric figures, images, and patterns, such as a wallpaper pattern. The definition can be made more precise by specifying what is meant by image or pattern, e.g., a function of position with values in a set of colors. For symmetry of physical objects, one may also want to take physical composition into account. The group of isometries of space induces a group action on objects in it.

The symmetry group is sometimes also called full symmetry group in order to emphasize that it includes the orientation-reversing isometries (like reflections, glide reflections and improper rotations) under which the figure is invariant. The subgroup of orientation-preserving isometries (i.e. translations, rotations, and compositions of these) which leave the figure invariant is called its proper symmetry group. The proper symmetry group of an object is equal to its full symmetry group if and only if the object is chiral (and thus there are no orientation-reversing isometries under which it is invariant).

R. Parthasarathy (born 1934) is an Indian poet, translator, critic, and editor.

Rajagopal Parthasarathy was born in 1934 at Tirupparaiturai near Tiruchchirappalli. He was educated at Don Bosco High School and Siddharth College , Mumbai and at Leeds University , UK , where he was British Council Scholar in 1963–64.

He was Lecturer in English Literature in Mumbai for ten years before joining Oxford University Press in 1971 as Regional Editor in Chennai. He moved to New Delhi in 1978. He is Associate Professor of English and Asian Studies at Skidmore College in Saratoga Springs , New York , USA .

His works include Poetry from Leeds in 1968 , Rough Passage brought out by Oxford University Press in 1977 , a long poem ( Preface "a book where all poems form part of a single poem, as it were" – R. Parthasarathy ) and edited Ten Twentieth-Century Indian Poets published by Oxford University Press in 1976 which went into Sixteenth Impression only in 2002.He translates from Tamil to English. His translation into modern English verse of the 5th-century Tamil epic, The Tale of the Anklet: An Epic of South India brought out by Columbia UP in 1993. It has received significant awards including the Sahitya Akademi Translation Prize in 1995 and The Association for Asian Studies, Inc. – A.K. Ramanujan Book Prize for Translation in 1996. He was awarded the Ulka Poetry Prize of Poetry India in 1966. He was a member of the University of Iowa Writing Program during 1978–79. He was member of the Advisory Board for English of the Sahitya Akademi – the National Academy of Letters , New Delhi , India .