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## Subgroup of a finitely generated nilpotent group [closed]

Let $G$ be a finitely generated nilpotent group. Then $G/[G,G]$ is finitely generated abelian group. Show that there exists a finite index subroup $H< G$ such that $H/[H,H]\simeq \mathbb{Z}^{r}$ for some $r$.

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 How do you know this is possible? – Simon Wadsley Aug 25 2011 at 12:23 Could you rephrase the question so it doesn't seem like a command (or a homework problem)? – S. Carnahan♦ Aug 25 2011 at 13:50 This is a homework problem (or possibly he is preparing for an algebra exam). Voted to close. – Mark Sapir Aug 25 2011 at 13:55