Obstruction to be conjugated by an automorphism for subgroups of an abelian group

54 Views Asked by At

Let $A$ be a finite abelian p-group( p being a prime number). Let $M,N$ be subgroup such that $M \simeq N$ and $A/M \simeq A/N$ as groups. Can I conclude that there is $\phi \in Aut(A)$ such that $\phi(M)=N$?