Universal power automorphism

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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.

Relation with other properties

Weaker properties