If $G/Z(G)$ is abelian then $G$ is abelian? 
If $G/Z(G)$ is abelian then $G$ is abelian. Give a counter example if this is not true.

I know that if $G/Z(G)$ is cyclic then $G$ is abelian. And $G/Z(G)$ cyclic implies that $G/Z(G)$ is abelian but I don't know how to do with $G/Z(G)$ only abelian.

Hint: Consider the quaternion group of 8 elements, $\{ \pm 1 , \pm i, \pm j, \pm k\}$.  This group is non abelian.   The center of the group is a group of order 2.   
