# Corollary of Timmesfeld's replacement theorem for abelian subgroups

Suppose $P$ is a group of prime power order. Let $\mathcal{A}(P)$ denote the set of abelian subgroups of maximum order in $P$. If $A \in \mathcal{A}(P)$, and $V$ is an $A$-invariant abelian subgroup of $P$. Then, $[V,A]C_A([V,A])$ is an abelian subgroup of maximum order.