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automorphism

An isomorphism from a group $G$ to itself. The set of all automorphisms of $G$ , written $\operatorname{Aut}(G)$ , forms a group under composition.

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Examples

In $\mathbb{Z}_6$ , negation $x\mapsto -x$ is an automorphism swapping $1\leftrightarrow5$ and $2\leftrightarrow4$ .