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Universal power map
From Groupprops
This article defines a function property, viz a property of functions from a group to itself
Contents |
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) = xn for all x in G.
Relation with other properties
Automorphisms and endomorphisms
- Universal power endomorphism is a universal power map that is also an endomorphism
- Universal power automorphism is a universal power map that is also an automorphism
For Abelian groups, all uniform power maps are endomorphisms.
