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Suppose that $G$ is a non-abelian group and $|G|=pq$ such that $p$ and $q$ are prime numbers and $N$ is normal subgroup of $G$ such that $|N|=q$ . show that $G'=N$.

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closed as off-topic by Travis, Shaun, Arnaud D., Paul Frost, Jendrik Stelzner May 24 at 17:39

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$|G/N|=p$ so $G/N$ is cyclic $\Rightarrow1\not= G'\subset N\Rightarrow G'=N$

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