Definition:Automorphism Group/Group

Definition
Let $\struct {S, *}$ be an algebraic structure.

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

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

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

The automorphism group of $S$ is often denoted $\Aut S$ or $\operatorname {\mathscr A} \paren S$.

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

Also see

 * Group of Automorphisms is Subgroup of Symmetric Group, where it is also demonstrated that $\Aut S$ is actually a group.