Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20E25

Retrieve articles in all journals with MSC (2000): 20E25


Additional Information

U. Meierfrankenfeld
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48840
Email: meier@math.msu.edu

B. Stellmacher
Affiliation: Mathematisches Seminar, Christian-Albrechts-Universität, D24098 Kiel, Germany
Email: stellmacher@math.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04541-8
PII: S 0002-9947(08)04541-8
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.