Let $\displaystyle A \cong C_n^{m}$ be an abelian group consisting of the direct product of $\displaystyle C_n$ $\displaystyle m$-times for $\displaystyle m \in \mathbb{N} \cup \{\infty\}$. Let $\displaystyle H \leq A$.

My question is this: if $\displaystyle \phi$ is an automorphism of $\displaystyle H$ then does $\displaystyle \phi$ extend to an automorphism of $\displaystyle A$? If not in general, what if $\displaystyle n$ is prime?