Automorphism group of a group
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
VIEW: Definitions built on this | Facts about this: (facts closely related to Automorphism group of a group, all facts related to Automorphism group of a group) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |[SHOW MORE]
The automorphism group of a group is defined as a group whose elements are all the automorphisms of the base group, and where the group operation is composition of automorphisms. In other words, it gets a group structure as a subgroup of the group of all permutations of the group.
Definition with symbols
The 'automorphism group of a group , denoted , is a set whose elements are automorphisms , and where the group multiplication is composition of automorphisms. In other words, its group structure is obtained as a subgroup of , the group of all permutations on .