Automorphism group of a group
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 .