Hello. I finding for correct proof of this statement: If group $G/Z(G)$ is cyclic, then $G$ is commutative.
Proof: $G/Z(G)$ is isomorphic to $In(G)$ that is cyclic, and than for every inner isomorphism $\gamma_a$ is $\gamma_a \gamma_b = \gamma_{ab} = \gamma_{ba} = \gamma_b \gamma_a$ and therefore for every $a,b \in G$ is $ab = ba$.
Is that proof complete, or I miss something? Thanks a lot for help.
