Automorphism

algebra

Definition

Automorphism

Let $X$ be a mathematical object with some specified structure. An automorphism of $X$ is an isomorphism $f:X\to X$.

Equivalently, it is a bijective structure-preserving map from $X$ to itself.

The set of all automorphisms of $X$ is often written $\mathrm{Aut}(X)$.

Examples include automorphisms of groups, vector spaces, fields, and graphs.