Definition:Automorphism Group/Group

Definition
Let $\left({S, *}\right)$ be an algebraic structure.

Let $\mathbb S$ be the set of automorphisms of $S$.

Then the algebraic structure $\left({\mathbb S, \circ}\right)$, where $\circ$ denotes composition of mappings, is called the automorphism group of $S$.

The structure $\left({S, *}\right)$ is usually a group. However, this is not necessary for this definition to be valid.

The automorphism group of $S$ is often denoted $\operatorname{Aut} \left({S}\right)$ or $\mathscr A \left({S}\right)$.

Also known as
The automorphism group is also known as the group of automorphisms.

Also see

 * Group of Automorphisms is Subgroup of Group of Permutations, where it is also demonstrated that $\operatorname{Aut} \left({S}\right)$ is actually a group.