On recognizability by spectrum of finite simple groups of types B n , C n , and 2 D n for n = 2 k

  • A. V. Vasil’ev
  • I. B. Gorshkov
  • M. A. Grechkoseeva
  • A. S. Kondrat’ev
  • A. M. Staroletov
Article

Abstract

The spectrum of a finite group is the set of its element orders. A group is said to be recognizable (by spectrum) if it is isomorphic to any finite group that has the same spectrum. A nonabelian simple group is called quasi-recognizable if every finite group with the same spectrum possesses a unique nonabelian composition factor and this factor is isomorphic to the simple group in question. We consider the problem of recognizability and quasi-recognizability for finite simple groups of types B n , C n , and 2 D n with n = 2 k .

Keywords

finite simple group spectrum of a group prime graph recognition by spectrum orthogonal group symplectic group 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. V. Vasil’ev
    • 1
  • I. B. Gorshkov
    • 2
  • M. A. Grechkoseeva
    • 1
  • A. S. Kondrat’ev
    • 3
  • A. M. Staroletov
    • 2
  1. 1.Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Institute of Mathematics and MechanicsUral Division of the Russian Academy of SciencesYekaterinburgRussia

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