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$\begingroup$

Please give me an example of a locally nilpotent group such that its derived subgroup is a p-group but its central factor is not torsion.

Homework

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    "It's central factor"? What central factor? Do you mean $\,G/Z(G)\,$?2012-10-28
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    Assuming that central factor means $G/Z(G)$, does a semidirect product of a quasicyclic $p$-group ${\mathbb Z}_{p^{\infty}}$ by an infinite cyclic group with action $x \mapsto x^{1+p}$ work?2012-10-29
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    yes Antonio. By central factor I mean G/Z(G)2012-10-31
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    Dear Derek, would you please explain more?2012-10-31
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    Dear Derek I can't show that your example is locally nilpotent. Would you please help me.2012-11-07

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