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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

REFERENCES

1.Passman, D. S., The algebraic structure of group rings, Pure and Applied Mathematics (Wiley-Interscience, New York, 1977).Google Scholar
2.Robinson, D. J. S., A course in the theory of groups, Second edition, Graduate Texts in Mathematics, Vol. 80 (Springer-Verlag, New York, 1996).CrossRefGoogle Scholar
3.Roseblade, J. E., Applications of the Artin–Rees lemma to group rings, in Symposia Mathematica, Vol. XVII (Convegno sui Gruppi Infiniti, INDAM, Roma, 1973), (Academic Press, London, 1976), 471–478.Google Scholar
4.Segal, D., Polycyclic groups, Cambridge Tracts in Mathematics, Vol. 82 (Cambridge University Press, Cambridge, England, UK, 1983).CrossRefGoogle Scholar
5.Šmel′kin, A. L., Polycyclic groups, Sibirsk. Mat. Z. 9 (1968), 234–235; English translation: Siberian Math. J., 9 (1968), 178.Google Scholar