A spectral sequence for fusion systems

Díaz Ramos, Antonio

doi:10.2140/agt.2014.14.349

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A spectral sequence for fusion systems

Antonio Díaz Ramos

Algebraic & Geometric Topology 14 (2014) 349–378

DOI: 10.2140/agt.2014.14.349

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

References

Publication

Received: 13 December 2012

Revised: 22 May 2013

Accepted: 29 May 2013

Preview posted: 5 December 2014

Published: 9 January 2014

Authors

Antonio Díaz Ramos
Departamento de Álgebra, Geometría y Topología Campus de Teatinos Universidad de Málaga 29071, Málaga Spain
http://agt.cie.uma.es/~adiaz

Volume 14, issue 1 (2014)