# Powering-invariance is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., powering-invariant subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about powering-invariant subgroup |Get facts that use property satisfaction of powering-invariant subgroup | Get facts that use property satisfaction of powering-invariant subgroup|Get more facts about transitive subgroup property

## Statement

Suppose are groups such that is a powering-invariant subgroup of and is a powering-invariant subgroup of . Then, is a powering-invariant subgroup of .