Algebraic & Geometric Topology

The normaliser decomposition for $p$–local finite groups

Assaf Libman

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.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 3 (2006), 1267-1288.

Dates
Accepted: 29 June 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796577

Digital Object Identifier
doi:10.2140/agt.2006.6.1267

Mathematical Reviews number (MathSciNet)
MR2253446

Zentralblatt MATH identifier
1128.55006

Citation

Libman, Assaf. The normaliser decomposition for $p$–local finite groups. Algebr. Geom. Topol. 6 (2006), no. 3, 1267--1288. doi:10.2140/agt.2006.6.1267. https://projecteuclid.org/euclid.agt/1513796577

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