On groups acting on contractible spaces with stabilizers of prime power order
On groups acting on contractible spaces with stabilizers of prime power order
Let F denote the class of finite groups, and let P denote the subclass consisting of groups of prime power order. We study group actions on topological spaces in which either (1) all stabilizers lie in P or (2) all stabilizers lie in F. We compare the classifying spaces for actions with stabilizers in F and P, the Kropholler hierarchies built on F and P, and group cohomology relative to F and to P. In terms of standard notations, we show that F C H1P C H1F, with all inclusions proper; that HF = HP; that FH*(G;?) = PH*(G;?); and that EpG is finite-dimensional if and only if EfG is finite-dimensional and every finite subgroup of G is in P
769-778
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
October 2010
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
Leary, Ian J. and Nucinkis, Brita E.A.
(2010)
On groups acting on contractible spaces with stabilizers of prime power order.
Journal of Group Theory, 13 (5), .
(doi:10.1515/JGT.2010.012).
Abstract
Let F denote the class of finite groups, and let P denote the subclass consisting of groups of prime power order. We study group actions on topological spaces in which either (1) all stabilizers lie in P or (2) all stabilizers lie in F. We compare the classifying spaces for actions with stabilizers in F and P, the Kropholler hierarchies built on F and P, and group cohomology relative to F and to P. In terms of standard notations, we show that F C H1P C H1F, with all inclusions proper; that HF = HP; that FH*(G;?) = PH*(G;?); and that EpG is finite-dimensional if and only if EfG is finite-dimensional and every finite subgroup of G is in P
Text
epg.pdf
- Author's Original
Text
epg.pdf
- Author's Original
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Submitted date: 9 March 2009
Accepted/In Press date: 9 March 2009
Published date: October 2010
Identifiers
Local EPrints ID: 65888
URI: http://eprints.soton.ac.uk/id/eprint/65888
ISSN: 1433-5883
PURE UUID: baf3bb85-20d7-4674-b1a1-e4d89f3e8e6f
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Date deposited: 25 Mar 2009
Last modified: 14 Mar 2024 02:56
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Author:
Brita E.A. Nucinkis
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