# Quotient-powering-invariance is quotient-transitive

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)
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## Statement

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

## Proof

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