#### 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 $k{C}_{G}\left(P\right)e$ 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
Primary: 20C20
##### Milestones
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