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A NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS

Published online by Cambridge University Press:  04 December 2009

GIOVANNI CUTOLO  and
HOWARD SMITH
GIOVANNI CUTOLO
Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia—Monte S. Angelo I-80126 Napoli, Italyhttp://www.dma.unina.it/cutolo e-mail: [email protected]
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA e-mail: [email protected]
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Abstract

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A subgroup H of a residually finite-p group G is almost p-closed in G if H has finite p′-index in 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 |H: H| takes on all possible values, including infinity, as H varies.

Keywords

20F1620E26
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 137 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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