$ZJ$-theorems for fusion systems
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- by Radha Kessar and Markus Linckelmann PDF
- Trans. Amer. Math. Soc. 360 (2008), 3093-3106 Request permission
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.References
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Additional Information
- Radha Kessar
- Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom
- MR Author ID: 614227
- Markus Linckelmann
- Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom
- MR Author ID: 240411
- Received by editor(s): October 3, 2005
- Received by editor(s) in revised form: March 23, 2006
- Published electronically: January 25, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 3093-3106
- MSC (2000): Primary 20C20
- DOI: https://doi.org/10.1090/S0002-9947-08-04275-X
- MathSciNet review: 2379788