Gillam's abelian-to-normal replacement theorem for metabelian groups

Statement
Suppose $$p$$ is a prime number and $$P$$ is a finite p-group. Suppose $$P$$ is a metabelian group, i.e., its derived length is at most two. Then, the following are true:


 * 1) For any abelian subgroup of maximum order $$A$$ in $$P$$, there exists an abelian normal subgroup $$B$$ of $$P$$ that is contained in the normal closure of $$A$$ in $$P$$ and has the same order as $$A$$.
 * 2) For any elementary abelian subgroup of maximum order $$A$$ in $$P$$, there exists a elementary abelian normal subgroup $$B$$ of $$P$$ that is contained in the normal closure of $$A$$ in $$P$$ and has the same order as $$A$$.