Suppose $\displaystyle A$ is a finite abelian group. Then is the quotient group $\displaystyle A/2A \cong A[2]$ where $\displaystyle A[2]$ denotes the set of 2 torsion elements in $\displaystyle A$ (that is, the elements $\displaystyle a \in A$ such that $\displaystyle 2a$ is the identity) ? I feel this should be easy to prove if it were true but haven't managed to get anywhere.