Vol. 305, No. 1, 2020

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Fusion systems of blocks of finite groups over arbitrary fields

Robert Boltje, Çisil Karagüzel and Deniz Yılmaz

Vol. 305 (2020), No. 1, 29–41
Abstract

To any block idempotent b of a group algebra kG of a finite group G over a field k of characteristic p > 0, Puig associated a fusion system and proved that it is saturated if the k-algebra kCG(P)e is split, where (P,e) is a maximal kGb-Brauer pair. We investigate in the nonsplit case how far the fusion system is from being saturated by describing it in an explicit way as being generated by the fusion system of a related block idempotent over a larger field together with a single automorphism of the defect group.

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Keywords
blocks of finite groups, fusion systems
Mathematical Subject Classification 2010
Primary: 20C20
Milestones
Received: 24 July 2019
Accepted: 2 October 2019
Published: 17 March 2020
Authors
Robert Boltje
Department of Mathematics
University of California
Santa Cruz, CA
United States
Çisil Karagüzel
Department of Mathematics
University of California
Santa Cruz, CA
United States
Deniz Yılmaz
Department of Mathematics
University of California
Santa Cruz, CA
United States