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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$ZJ$-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.
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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