Algebraic & Geometric Topology

The normaliser decomposition for $p$–local finite groups

Assaf Libman

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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.

Article information

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

Received: 4 February 2005
Accepted: 29 June 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R35: Classifying spaces of groups and $H$-spaces 55P05: Homotopy extension properties, cofibrations

homology decomposition $p$–local finite groups


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.

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