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.
Other articles related to "symmetry group, group, symmetry, groups, symmetry groups":
... 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 ... 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:
“I cant think of a single supposedly Black issue that hasnt wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)
“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 (17881824)