# Finite implies local powering-invariant

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., finite subgroup) must also satisfy the second subgroup property (i.e., local powering-invariant subgroup)

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## Statement

Suppose is a group and is a finite subgroup of . Then, is a local powering-invariant subgroup of : for any and such that the solution to is unique for , we must have .