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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cohomology and finite subgroups of profinite groups


Authors: Pham Anh Minh and Peter Symonds
Journal: Proc. Amer. Math. Soc. 132 (2004), 1581-1588
MSC (2000): Primary 20J06, 17B50
Published electronically: November 4, 2003
MathSciNet review: 2051117
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove two theorems linking the cohomology of a pro-$p$ group $G$ with the conjugacy classes of its finite subgroups.

The number of conjugacy classes of elementary abelian $p$-subgroups of $G$ is finite if and only if the ring $H^{*}(G,\mathbb{Z} /p)$ is finitely generated modulo nilpotent elements.

If the ring $H^{*}(G,\mathbb{Z} /p)$ is finitely generated, then the number of conjugacy classes of finite subgroups of $G$ is finite.


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Additional Information

Pham Anh Minh
Affiliation: Department of Mathematics, College of Science, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Address at time of publication: Inst. Hautes Études Sci., Le Bois-Marie, 35 Route de Chartres, F-91440 Bures-sur-Yvette, France
Email: paminh@dng.vnn.vn

Peter Symonds
Affiliation: Department of Mathematics, U.M.I.S.T., P.O. Box 88, Manchester M60 1QD, England
Email: Peter.Symonds@umist.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07250-2
PII: S 0002-9939(03)07250-2
Received by editor(s): November 1, 2002
Received by editor(s) in revised form: February 9, 2003
Published electronically: November 4, 2003
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society