# Universal power automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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## Definition

### Symbol-free definition

An automorphism of a group is termed a universal power automorphism or uniform power automorphism if it is also a universal power map: it can be viewed as taking the $n^{th}$ power for some integer $n$.

### Definition with symbols

An automorphism $\sigma$ of a group $G$ is termed a universal power automorphism if there exists an integer $n$ such that $\sigma(g) = g^n$ for all $g \in G$.