Universal power map

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This article defines a function property, viz a property of functions from a group to itself

Definition

Symbol-free definition

A universal power map or uniform power map is a function from a group to itself such that there exists an integer for which the function is simply raising to the power of that integer.

Definition with symbols

A function f on a group G is termed a universal power map or uniform power map if there exists an integer n such that f(x) = x^n for all x in G.

Relation with other properties

Automorphisms and endomorphisms

For Abelian groups, all uniform power maps are endomorphisms.

Particular cases