Show that if $G$ is a finite nonsolvable group then $G$ contains a nontrivial subgroup $H$ such that $\left[H,H\right]=H$.
If $G$ is a finite nonsolvable group then $G$ contains a nontrivial subgroup $H$ such that $\left[H,H\right]=H$.
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abstract-algebra
group-theory
finite-groups
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0I assume that $H$ should be nontrivial, since $1$ holds this property in every group. – 2012-10-07
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0Is $G$ assumed to be *finite*? – 2012-10-07
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0Yes, $G$ be finite – 2012-10-07