Let $G$ be an abelian group such that the Schur multiplier $M(G)=\mathbb{Z}_p\times \mathbb{Z}_p$.
Can we say that $G$ has a subgroup isomorphic to $\mathbb{Z}_p\times \mathbb{Z}_p.$
I have seen in many groups this relation holds, what can we say in general? I don't know that how to prove this or contradict. Please help me.