Fusion systems of blocks of finite groups over arbitrary fields

Robert Boltje, Çisil Karagüzel and Deniz Yılmaz

Vol. 305 (2020), No. 1, 29–41

DOI: 10.2140/pjm.2020.305.29

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 $k{C}_G\left(P\right)e$ is split, where $\left(P,e\right)$ 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.

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