Normal subsystems of fusion systems

In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether on...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2011-08, Vol.84 (1), p.137-158
Main Author: Craven, David A.
Format: Article
Language:English
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Summary:In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdr004