Siberian Mathematical Journal

, Volume 46, Issue 3, pp 396–404 | Cite as

On Connection Between the Structure of a Finite Group and the Properties of Its Prime Graph

  • A. V. Vasil’ev
Article

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 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Vasil’ev
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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