$F$-stability in finite groups
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- by U. Meierfrankenfeld and B. Stellmacher PDF
- Trans. Amer. Math. Soc. 361 (2009), 2509-2525 Request permission
Abstract:
Let $G$ be a finite group, $S \in Syl_p(G)$, 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
- D. Bundy, N. Hebbinghaus, and B. Stellmacher, The local $C(G,T)$ theorem, J. Algebra 300 (2006), no. 2, 741–789. MR 2228220, DOI 10.1016/j.jalgebra.2005.08.040
- Robert M. Guralnick, Ross Lawther, and Gunter Malle, The 2F-modules for nearly simple groups, J. Algebra 307 (2007), no. 2, 643–676. MR 2275366, DOI 10.1016/j.jalgebra.2006.10.011
- Robert M. Guralnick and Gunter Malle, Classification of $2F$-modules. I, J. Algebra 257 (2002), no. 2, 348–372. MR 1947326, DOI 10.1016/S0021-8693(02)00526-4
- Robert M. Guralnick and Gunter Malle, Classification of $2F$-modules. II, Finite groups 2003, Walter de Gruyter, Berlin, 2004, pp. 117–183. MR 2125071
- Hans Kurzweil and Bernd Stellmacher, The theory of finite groups, Universitext, Springer-Verlag, New York, 2004. An introduction; Translated from the 1998 German original. MR 2014408, DOI 10.1007/b97433
- R. Lawther, $2F$-modules, abelian sets of roots and 2-ranks, J. Algebra 307 (2007), no. 2, 614–642. MR 2275365, DOI 10.1016/j.jalgebra.2006.10.012
- U. Meierfrankenfeld, B. Stellmacher, G. Stroth, The structure theorem, in preparation.
- Ch. W. Parker, G. Parmeggiani, and B. Stellmacher, The $P$!-theorem, J. Algebra 263 (2003), no. 1, 17–58. MR 1974077, DOI 10.1016/S0021-8693(03)00075-9
- Bernd Stellmacher, On the $2$-local structure of finite groups, Groups, combinatorics & geometry (Durham, 1990) London Math. Soc. Lecture Note Ser., vol. 165, Cambridge Univ. Press, Cambridge, 1992, pp. 159–182. MR 1200259, DOI 10.1017/CBO9780511629259.017
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
- Received by editor(s): May 16, 2006
- Received by editor(s) in revised form: May 3, 2007
- Published electronically: December 16, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 2509-2525
- MSC (2000): Primary 20E25
- DOI: https://doi.org/10.1090/S0002-9947-08-04541-8
- MathSciNet review: 2471927