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The normaliser decomposition for $p$–local finite groups

Assaf Libman

Algebraic & Geometric Topology 6 (2006) 1267–1288

arXiv: 0904.3452

Abstract

We construct an analogue of the normaliser decomposition for p–local finite groups (S,,) with respect to collections of –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