Definition:Automorphism Group/Group

Theorem
The set of automorphisms of a group $$G$$ is itself a group, under composition of mappings, and is denoted $$\mathrm{Aut} \left({G}\right)$$.

Proof
An automorphism is an isomorphism $$\phi: G \to G$$ from an algebraic structure $$G$$ to itself.

We check the group axioms.