Transactions of the American Mathematical Society

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



$ F$-stability in finite groups

Authors: U. Meierfrankenfeld and B. Stellmacher
Journal: Trans. Amer. Math. Soc. 361 (2009), 2509-2525
MSC (2000): Primary 20E25
Published electronically: December 16, 2008
MathSciNet review: 2471927
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Abstract: Let $ G$ be a finite group, $ S \in \mathit {Syl}_p(G)$, and $ \mathcal S$ be the set subgroups containing $ S$. For $ M \in \mathcal S$ and $ V = \Omega_1Z(O_p(M))$, the paper discusses the action of $ M$ on $ V$. Apart from other results, it is shown that for groups of parabolic characteristic $ p$ either $ S$ is contained in a unique maximal $ p$-local subgroup, or there exists a maximal $ p$-local subgroup in $ M \in \mathcal S$ such that $ V$ is a nearly quadratic 2F-module for $ M$.

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Additional Information

U. Meierfrankenfeld
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48840

B. Stellmacher
Affiliation: Mathematisches Seminar, Christian-Albrechts-Universität, D24098 Kiel, Germany

Received by editor(s): May 16, 2006
Received by editor(s) in revised form: May 3, 2007
Published electronically: December 16, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.