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), 896-904. (doi:10.1112/blms/bdq045).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1112/blms/bdq045
ISSNs: 0024-6093 (print)
1469-2120 (electronic)
Subjects: Q Science > QA Mathematics
Divisions : Faculty of Social and Human Sciences > Mathematical Sciences > Pure Mathematics
ePrint ID: 199421
Accepted Date and Publication Date:
October 2010Published
17 June 2010Made publicly available
Date Deposited: 18 Oct 2011 11:01
Last Modified: 31 Mar 2016 13:45
Topics in Geometric Group Theory
Funded by: National Science Foundation (0706259)
1 July 2007 to 30 June 2011
Cohomology, curvature, classifying spaces and symmetry
Funded by: National Science Foundation (0804226)
15 July 2008 to 30 June 2011

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