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Abstract
We build a spectral sequence converging to the cohomology of a fusion system
with a strongly closed subgroup. This spectral sequence is related to the
Lyndon–Hochschild–Serre spectral sequence and coincides with it for the case of an
extension of groups. Nevertheless, the new spectral sequence applies to more general
situations like finite simple groups with a strongly closed subgroup and exotic fusion
systems with a strongly closed subgroup. We prove an analogue of a result of
Stallings in the context of fusion preserving homomorphisms and deduce Tate’s
p –nilpotency
criterion as a corollary.
Keywords
Lyndon–Hochschild–Serre spectral sequence, fusion system,
strongly closed subgroup, Tate's nilpotency criterion
Mathematical Subject Classification 2010
Primary: 55T10
Secondary: 55R35, 20D20
Publication
Received: 13 December 2012
Revised: 22 May 2013
Accepted: 29 May 2013
Preview posted: 5 December 2014
Published: 9 January 2014