# Characteristic subgroup of abelian group implies intermediately 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., characteristic subgroup of abelian group) must also satisfy the second subgroup property (i.e., intermediately powering-invariant subgroup)

View all subgroup property implications | View all subgroup property non-implications

Get more facts about characteristic subgroup of abelian group|Get more facts about intermediately powering-invariant subgroup

## Statement

Suppose is an abelian group and are subgroups of with . Suppose that is a characteristic subgroup of . Then, is also a powering-invariant subgroup of .