Abstract
Given a p-block B of a finite group with defect group P and fusion system \({\mathcal {F}}\) on P, we show that the rank of the group \(P/\mathfrak {foc}({\mathcal {F}})\) is invariant under stable equivalences of Morita type. The main ingredients are the \(*\)-construction, due to Broué and Puig, a theorem of Weiss on linear source modules, arguments of Hertweck and Kimmerle applying Weiss’ theorem to blocks, and connections with integrable derivations in the Hochschild cohomology of block algebras.
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The present work is partially funded by the EPSRC grant EP/M02525X/1.
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Linckelmann, M. (2018). On Automorphisms and Focal Subgroups of Blocks. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_9
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