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This article is cited in 175 scientific papers (total in 175 papers)
An Adjacency Criterion for the Prime Graph of a Finite Simple Group
A. V. Vasil'ev, E. P. Vdovin Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders on these sets; the information obtained is collected in tables. We consider several applications of these results to various problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Keywords:
finite group, finite simple group, group of Lie type, spectrum of a finite group, recognition by spectrum, prime graph of a finite group, independence number of a prime graph, 2-independence number of a prime graph.
Received: 30.05.2005
Citation:
A. V. Vasil'ev, E. P. Vdovin, “An Adjacency Criterion for the Prime Graph of a Finite Simple Group”, Algebra Logika, 44:6 (2005), 682–725; Algebra and Logic, 44:6 (2005), 381–406
Linking options:
https://www.mathnet.ru/eng/al137 https://www.mathnet.ru/eng/al/v44/i6/p682
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Abstract page: | 1494 | Full-text PDF : | 445 | References: | 108 | First page: | 1 |
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