Subgroup families controlling p-local finite groups

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dc.creatorBroto, Carles
dc.creatorCastellana, Natalia
dc.creatorGrodal, Jesper
dc.creatorLevi, Ran
dc.creatorOliver, Bob
dc.date2004-03-02
dc.date2005-02-16
dc.date.accessioned2026-07-07T07:37:19Z
dc.date.available2026-07-07T07:37:19Z
dc.descriptionA p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we examine which subgroups control this structure. More precisely, we prove that the question of whether an abstract fusion system F over a finite p-group S is saturated can be determined by just looking at smaller classes of subgroups of S. We also prove that the homotopy type of the classifying space of a given p-local finite group is independent of the family of subgroups used to define it, in the sense that it remains unchanged when that family ranges from the set of F-centric F-radical subgroups (at a minimum) to the set of F-quasicentric subgroups (at a maximum). Finally, we look at constrained fusion systems, analogous to p-constrained finite groups, and prove that they in fact all arise from groups.
dc.description32 pages. To appear in Proc. London Math Soc
dc.identifierhttps://arxiv.org/abs/math/0403042
dc.identifierhttp://arxiv.org/abs/math/0403042
dc.identifierProc. London Math. Soc. (3) 91 (2005) no. 2, 325--354
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120738
dc.subjectAlgebraic Topology
dc.subjectGroup Theory
dc.subject55R35 (Primary) 55R40, 20D20 (Secondary)
dc.titleSubgroup families controlling p-local finite groups
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