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.

Read more about Symmetry Group: Introduction, One Dimension, Two Dimensions, Three Dimensions, Symmetry Groups in General

### Other articles related to "symmetry group, group, symmetry, groups, symmetry groups":

**Symmetry Group**s in General

... See also Automorphism In wider contexts, a

**symmetry group**may be any kind of transformation

**group**, or automorphism

**group**... Conversely, specifying the

**symmetry**can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it this is one way of looking at the Erlangen programme ... For example, automorphism

**groups**of certain models of finite geometries are not "

**symmetry groups**" in the usual sense, although they preserve

**symmetry**...

### Famous quotes containing the words group and/or symmetry:

“He hung out of the window a long while looking up and down the street. The world’s second metropolis. In the brick houses and the dingy lamplight and the voices of a *group* of boys kidding and quarreling on the steps of a house opposite, in the regular firm tread of a policeman, he felt a marching like soldiers, like a sidewheeler going up the Hudson under the Palisades, like an election parade, through long streets towards something tall white full of colonnades and stately. Metropolis.”

—John Dos Passos (1896–1970)

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)