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Abstract
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To any block idempotent
of a group algebra
of a finite group
over a field
of
characteristic
,
Puig associated a fusion system and proved that it is saturated if the
-algebra
is split, where
is a maximal
-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
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Mathematical Subject Classification 2010
Primary: 20C20
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Milestones
Received: 24 July 2019
Accepted: 2 October 2019
Published: 17 March 2020
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