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Groups possessing extensive hierarchical decompositions

Januszkiewicz, T., Kropholler, P.H. and Leary, I.J. (2010) Groups possessing extensive hierarchical decompositions Bulletin of the London Mathematical Society, 42, (5), pp. 896-904. (doi:10.1112/blms/bdq045).

Record type: Article

Abstract

The class HF is the smallest class of groups that contains all finite groups and is closed under the following operator: whenever G admits a finite-dimensional contractible G-CW-complex in which all stabilizers are in HF, then G is itself in HF. The class HF admits a natural filtration by the ordinals. For each countable ordinal we show that there is a countable group that is in HF but has not arisen by stage alpha of this filtration. Previously this result was known only for alpha equal to 0, 1, and 2. The groups that we construct contain torsion. We also review the construction of a torsion-free countable group in HF that is not in stage 2 of the filtration.

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More information

e-pub ahead of print date: 17 June 2010
Published date: October 2010
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 199421
URI: http://eprints.soton.ac.uk/id/eprint/199421
ISSN: 0024-6093
PURE UUID: 7dae0a77-d744-43d0-bacf-040564a89c0a
ORCID for I.J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

Catalogue record

Date deposited: 18 Oct 2011 11:01
Last modified: 18 Jul 2017 11:16

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Contributors

Author: T. Januszkiewicz
Author: P.H. Kropholler
Author: I.J. Leary ORCID iD

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