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Algebra Logika, 2005, Volume 44, Number 6, Pages 682–725 (Mi al137)  

This article is cited in 125 scientific papers (total in 125 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

Full text: PDF file (401 kB)
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English version:
Algebra and Logic, 2005, 44:6, 381–406

Bibliographic databases:

UDC: 512.542
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

Citation in format AMSBIB
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\paper An Adjacency Criterion for the Prime Graph of a~Finite Simple Group
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\pages 682--725
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    This publication is cited in the following articles:
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    38. A. V. Vasil'ev, E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group”, Algebra and Logic, 50:4 (2011), 291–322  mathnet  crossref  mathscinet  zmath  isi
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