A spectral sequence for fusion systems

Díaz Ramos, Antonio¹

¹Departamento de Álgebra, Geometría y Topología, Campus de Teatinos, Universidad de Málaga, 29071, Málaga, Spain

Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 349-378

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.349

Classification : 55T10, 55R35, 20D20
Keywords: Lyndon–Hochschild–Serre spectral sequence, fusion system, strongly closed subgroup, Tate's nilpotency criterion

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