Homology, Homotopy and Applications

Volume 14 (2012)

Number 2

Homology decompositions and groups inducing fusion systems

Pages: 167 – 187

DOI: https://dx.doi.org/10.4310/HHA.2012.v14.n2.a10

Authors

Assaf Libman (Department of Mathematical Sciences, King’s College, Aberdeen, Scotland, United Kingdom)

Nora Seeliger (Max-Planck-Institut für Mathematik, Bonn, Germany)

Abstract

We relate the construction of groups which realize saturated fusion systems and signaliser functors with homology decompositions of $p$-local finite groups. We prove that the cohomology ring of Robinson’s construction is in some precise sense very close to the cohomology ring of the fusion system it realizes.

Keywords

fusion system, signalizer functor, homology decomposition

2010 Mathematics Subject Classification

20Jxx, 55R35

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Published 4 December 2012