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On Automorphisms and Focal Subgroups of Blocks

  • Markus LinckelmannEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

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.

Notes

Acknowledgements

The present work is partially funded by the EPSRC grant EP/M02525X/1.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsCity, University of LondonNorthampton Square, LondonUK

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