Definition:Automorphism (Abstract Algebra)

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

This applies to the term isomorphism as used both in the sense of bijective homomorphism as well as that of an order isomorphism.

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.