Volume 6, issue 3 (2006)

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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 $\left(S,\mathsc{ℱ},\mathsc{ℒ}\right)$ with respect to collections of $\mathsc{ℱ}$–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