Possible Duplicate:
There does not exist a group $G$ such that $|G/Z(G)|=pq$ for $p,q$ prime.
Let $p$ and $q$ prime numbers, with $p and $p \nmid (q-1)$. Show that do not exist group $G$ where $\left\lvert\frac{G}{Z(G)}\right\rvert=pq.$
Possible Duplicate:
There does not exist a group $G$ such that $|G/Z(G)|=pq$ for $p,q$ prime.
Let $p$ and $q$ prime numbers, with $p and $p \nmid (q-1)$. Show that do not exist group $G$ where $\left\lvert\frac{G}{Z(G)}\right\rvert=pq.$
Use this Fact: If $G/Z(G)$ is cyclic, then G is abelian.