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S3-free 2-fusion systems

Part of: Fiber spaces and bundles Representation theory of groups

Published online by Cambridge University Press:  05 December 2012

Michael Aschbacher
Michael Aschbacher*
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA ([email protected])
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Abstract

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We develop a theory of 2-fusion systems of even characteristic, and use that theory to show that all S3-free saturated 2-fusion systems are constrained. This supplies a new proof of Glauberman's Theorem on S4-free groups and its various corollaries.

Keywords

finite groupsfusion systemsSylow subgroups

MSC classification

Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 55R35: Classifying spaces of groups and $H$-spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 27 - 48
Copyright
Copyright © Edinburgh Mathematical Society 2012

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