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$F$-stability in finite groups.
- Source :
-
Transactions of the American Mathematical Society . Dec2008, Vol. 361 Issue 5, p2509-2525. 17p. - Publication Year :
- 2008
-
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 $M$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 361
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 36232180
- Full Text :
- https://doi.org/10.1090/S0002-9947-08-04541-8