We construct an analogue of the normaliser decomposition for –local finite groups with respect to collections of –centric subgroups and collections of elementary abelian subgroups of . This enables us to describe the classifying space of a –local finite group, before –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.
"The normaliser decomposition for $p$–local finite groups." Algebr. Geom. Topol. 6 (3) 1267 - 1288, 2006. https://doi.org/10.2140/agt.2006.6.1267