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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 3, Pages 511–522
(Mi smj983)
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This article is cited in 92 scientific papers (total in 92 papers)
On connection between the structure of a finite group and the properties of Its prime graph
A. V. Vasil'ev Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
It is shown that the condition of nonadjacency of 2 and at least one odd prime in the Gruenberg–Kegel graph of a finite group $G$ under some natural additional conditions suffices to describe the structure of $G$; in particular, to prove that $G$ has a unique nonabelian composition factor. Applications of this result to the problem of recognition of finite groups by spectrum are also considered.
Keywords:
finite group, finite simple group, prime graph of a finite group, spectrum of a group, recognition by spectrum.
Received: 29.11.2004
Citation:
A. V. Vasil'ev, “On connection between the structure of a finite group and the properties of Its prime graph”, Sibirsk. Mat. Zh., 46:3 (2005), 511–522; Siberian Math. J., 46:3 (2005), 396–404
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https://www.mathnet.ru/eng/smj983 https://www.mathnet.ru/eng/smj/v46/i3/p511
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Abstract page: | 924 | Full-text PDF : | 294 | References: | 87 |
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