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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 74–83
(Mi timm224)
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This article is cited in 6 scientific papers (total in 6 papers)
On the intersections of solvable Hall subgroups in finite groups
E. P. Vdovin, V. I. Zenkov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
The following conjecture is considered: if a finite group $G$ possesses a solvable $\pi$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_\pi(G)$ holds. Under additional conditions on $G$ and $H$, it is shown that a minimal counterexample to this conjecture must be an almost simple group of Lie type.
Keywords:
solvable Hall subgroup, finite simple group, $\pi$-radical.
Received: 10.12.2008
Citation:
E. P. Vdovin, V. I. Zenkov, “On the intersections of solvable Hall subgroups in finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 74–83; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S234–S243
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https://www.mathnet.ru/eng/timm224 https://www.mathnet.ru/eng/timm/v15/i2/p74
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Abstract page: | 450 | Full-text PDF : | 108 | References: | 91 | First page: | 4 |
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