Group theory/Center/Properties/Exercise

Let $G$ be a group with center $Z(G)$. Prove the following statements:

a) $G$ is Abelian if and only if $G/Z(G)$ is cyclic.

b) The index of $Z(G)$ in $G$ is not a prime number.

c) If the order of $G$ is $pq$ for two prime number $p$ and $q$, then $G$ is Abelian, or $Z(G)$ is trivial.

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