Cohomology of linking systems with twisted coefficients by a $p$-solvable action

In this paper, we study the cohomology of the geometric realization of linking systems with twisted coefficients. More precisely, given a prime $p$ and a $p$-local finite group $(S,\mathcal{F},\mathcal{L})$, we compare the cohomology of $\mathcal{L}$ with twisted coefficients with the submodule of $\mathcal{F}^c$-stable elements in the cohomology of $S$. We start with the particular case of constrained fusion systems. Then, we study the case of $p$-solvable actions on the coefficients.

Keywords

fusion system, $p$-local finite group, cohomology with twisted coefficients, group cohomology

2010 Mathematics Subject Classification

20D20, 20J06, 20J15, 55R35, 55R40

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Received 15 February 2016

Published 9 August 2017