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On Bredon homology of elementary amenable groups

Authors: Ramón J. Flores and Brita E. A. Nucinkis
Journal: Proc. Amer. Math. Soc. 135 (2007), 5-11
MSC (2000): Primary 20J05, 18G20
Published electronically: August 16, 2006
MathSciNet review: 2280168
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Abstract: We show that for elementary amenable groups the Hirsch length is equal to the Bredon homological dimension. This also implies that countable elementary amenable groups admit a finite-dimensional model for $ \underline{E}G$ of dimension less than or equal to the Hirsch length plus one. Some remarks on groups of type $ {\operatorname{FP}}_{\infty}$ are also made.

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Ramón J. Flores
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Barcelona, E 08193 Bellaterra, Spain
Address at time of publication: Departamento de Estadística, Universidad Carlos III, Campus de Colmen- arejo, 22 28270 Colmenarejo (Madrid), Spain

Brita E. A. Nucinkis
Affiliation: School of Mathematics, University of Southampton, Southampton, SO 17 1BJ, United Kingdom

Keywords: Elementary amenable group, Bredon homology
Received by editor(s): July 20, 2005
Published electronically: August 16, 2006
Additional Notes: This work was partially supported by MCYT grant BFM2001-2035
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2006 American Mathematical Society