# Quotient-powering-invariance is quotient-transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., quotient-powering-invariant subgroup) satisfying a subgroup metaproperty (i.e., quotient-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 quotient-powering-invariant subgroup |Get facts that use property satisfaction of quotient-powering-invariant subgroup | Get facts that use property satisfaction of quotient-powering-invariant subgroup|Get more facts about quotient-transitive subgroup property

## Statement

Suppose is a group and are normal subgroups of with contained inside . Suppose that is a quotient-powering-invariant subgroup of and is a quotient-powering-invariant subgroup of the quotient group . Then, is a quotient-powering-invariant subgroup of .

## Related facts

- Powering-invariance is not quotient-transitive
- Powering-invariant over quotient-powering-invariant implies powering-invariant

## Proof

The proof is fairly straightforward.**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]