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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 $\left\lvert\frac{G}{Z(G)}\right\rvert=pq.$

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    Isn't this the same as http://math.stackexchange.com/questions/21448$0$/there-does-not-exist-a-group-g-such-that-g-zg-pq-for-p-q-prime which you asked yesterday?2012-10-17

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Use this Fact: If $G/Z(G)$ is cyclic, then G is abelian.

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    the group...????????????2012-10-17