Symmetry group
Symmetry groups [ edit ] Main article: Symmetry group See also: Molecular symmetry , Space group , Point group , and Symmetry in physics The (2,3,7) triangle group, a hyperbolic reflection group, acts on this tiling of the hyperbolic plane [50] Symmetry groups are groups consisting of symmetries of given mathematical objects, principally geometric entities, such as the symmetry group of the square given as an introductory example above, although they also arise in algebra such as the symmetries among the roots of polynomial equations dealt with in Galois theory (see below). [51] Conceptually, group theory can be thought of as the study of symmetry. [p] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element can be associated to some operation ...