The normaliser decomposition for p–local finite groups

Libman, Assaf

doi:10.2140/agt.2006.6.1267

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The normaliser decomposition for $p$–local finite groups

Assaf Libman

Algebraic & Geometric Topology 6 (2006) 1267–1288

DOI: 10.2140/agt.2006.6.1267

arXiv: 0904.3452

Abstract

We construct an analogue of the normaliser decomposition for $p$ –local finite groups $(S, ℱ, ℒ)$ with respect to collections of $ℱ$ –centric subgroups and collections of elementary abelian subgroups of $S$ . This enables us to describe the classifying space of a $p$ –local finite group, before $p$ –completion, as the homotopy colimit of a diagram of classifying spaces of finite groups whose shape is a poset and all maps are induced by group monomorphisms.

Keywords

homology decomposition, $p$–local finite groups

Mathematical Subject Classification 2000

Primary: 55R35, 55P05

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Publication

Received: 4 February 2005

Accepted: 29 June 2006

Published: 11 September 2006

Authors

Assaf Libman
Department of Mathematical Sciences King’s College University of Aberdeen Aberdeen AB24 3UE Scotland United Kingdom

Volume 6, issue 3 (2006)