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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ ZJ$-theorems for fusion systems


Authors: Radha Kessar and Markus Linckelmann
Journal: Trans. Amer. Math. Soc. 360 (2008), 3093-3106
MSC (2000): Primary 20C20
Published electronically: January 25, 2008
MathSciNet review: 2379788
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Abstract: For $ p$ an odd prime, we generalise the Glauberman-Thompson $ p$-nilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We define a notion of $ Qd(p)$-free fusion systems and show that if $ \mathcal{F}$ is a $ Qd(p)$-free fusion system on some finite $ p$-group $ P$, then $ \mathcal{F}$ is controlled by $ W(P)$ for any Glauberman functor $ W$, generalising Glauberman's $ ZJ$-theorem (Glauberman, 1968) to arbitrary fusion systems.


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Additional Information

Radha Kessar
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom

Markus Linckelmann
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04275-X
PII: S 0002-9947(08)04275-X
Received by editor(s): October 3, 2005
Received by editor(s) in revised form: March 23, 2006
Published electronically: January 25, 2008
Article copyright: © Copyright 2008 American Mathematical Society