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This article is cited in 23 scientific papers (total in 23 papers)
The $D_\pi$-property in finite simple groups
D. O. Revin Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
Let $\pi$ be some set of primes. A finite group is said to possess the $D_\pi$-property if all of its maximal $\pi$-subgroups are conjugate. It is not hard to show that this property is equivalent to satisfaction of the complete analog of Sylow's theorem for Hall $\pi$-subgroups of a group. In the paper, we bring to a close an arithmetic description of finite simple groups with the $D_\pi$-property, for any set $\pi$ of primes. Previously, it was proved that a finite group possesses the $D_\pi$-property iff each composition factor of the group has this property. Therefore, the results obtained mean in fact that the question of whether a given group enjoys the $D_\pi$-property becomes purely arithmetic.
Keywords:
finite group, $D_\pi$-property, Sylow theorem.
Received: 27.08.2007 Revised: 09.01.2008
Citation:
D. O. Revin, “The $D_\pi$-property in finite simple groups”, Algebra Logika, 47:3 (2008), 364–394; Algebra and Logic, 47:3 (2008), 210–227
Linking options:
https://www.mathnet.ru/eng/al363 https://www.mathnet.ru/eng/al/v47/i3/p364
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Abstract page: | 711 | Full-text PDF : | 156 | References: | 112 | First page: | 5 |
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