Definition:Automorphism (Abstract Algebra)

An automorphism is an isomorphism from an algebraic structure to itself.

Group Automorphism
If $$\left({S, \circ}\right)$$ is a group, then an automorphism $$\phi: \left({S, \circ}\right) \to \left({S, \circ}\right)$$ is called a group automorphism.