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An Adjacency Criterion for the Prime Graph of a Finite Simple Group

Authors
  • Vasiliev, A. V.
  • Vdovin, E. P.
Type
Published Article
Journal
Algebra and Logic
Publisher
Kluwer Academic Publishers-Consultants Bureau
Publication Date
Nov 01, 2005
Volume
44
Issue
6
Pages
381–406
Identifiers
DOI: 10.1007/s10469-005-0037-5
Source
Springer Nature
Keywords
License
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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.

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