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
$\begingroup$
$\endgroup$
5
-
$\begingroup$ "It's central factor"? What central factor? Do you mean $\,G/Z(G)\,$? $\endgroup$– DonAntonioOct 28, 2012 at 14:19
-
$\begingroup$ 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? $\endgroup$– Derek HoltOct 29, 2012 at 10:23
-
$\begingroup$ yes Antonio. By central factor I mean G/Z(G) $\endgroup$– MitraOct 31, 2012 at 14:48
-
$\begingroup$ Dear Derek, would you please explain more? $\endgroup$– MitraOct 31, 2012 at 14:55
-
$\begingroup$ Dear Derek I can't show that your example is locally nilpotent. Would you please help me. $\endgroup$– MitraNov 7, 2012 at 12:26
Add a comment
|