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G. Cutolo and H. Smith
A note on polycyclic residually finite-p groups
Glasg. Math. J., 52, (2010), pp. 137–143.
doi: 10.1017/S001708950999022X
MathSciNet Zentralblatt Abstract Full Text
Abstract
A subgroup $H$ of a residually finite-$p$ group $G$ is almost $p$-closed in $G$ if $H$ has finite $p'$-index in $\overline H$, its closure with respect to the pro-$p$ topology on $G$. We characterise polycyclic residually finite-$p$ groups in which all subgroups are almost $p$-closed and discuss a few conditions that are sufficient for particular subgroups $H$ to be almost $p$-closed. We also present, for each prime $p$, an example of a polycyclic residually $p$ group $G$ for which $|\overline H:H|$ takes on all possible values, including infinity, as $H$ varies.
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