\begin{definition}[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.
Hence an '''automorphism''' is a permutation which is either a homomorphism or an order isomorphism, depending on context.
\end{definition}