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Sparse fusion systems

Part of: Representation theory of groups

Published online by Cambridge University Press:  19 November 2012

Adam Glesser
Adam Glesser*
Affiliation:
Department of Mathematics, California State University Fullerton, Fullerton, CA 92831, USA (algesser@fullerton.edu)
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Abstract

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We define sparse saturated fusion systems and show that, for odd primes, sparse systems are constrained. This simplifies the proof of the Glauberman–Thompson p-Nilpotency Theorem for fusion systems and a related theorem of Stellmacher. We then define a more restrictive class of saturated fusion systems, called extremely sparse systems, that are constrained for all primes.

Keywords

fusion systemsp-nilpotencygroupssparse

MSC classification

Secondary: 20C20: Modular representations and characters 20D15: Nilpotent groups, $p$-groups 20D99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 135 - 150
Copyright
Copyright © Edinburgh Mathematical Society 2012

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