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Siberian Mathematical Journal

, 50:965 | Cite as

On finite groups isospectral to simple symplectic and orthogonal groups

  • A. V. Vasil’ev
  • M. A. Grechkoseeva
  • V. D. Mazurov
Article

Abstract

The spectrum of a finite group is the set of its element orders. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field of an arbitrary positive characteristic p. It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over a field of the same characteristic p.

Keywords

finite group spectrum of a group simple group symplectic group orthogonal group composition factor 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. V. Vasil’ev
    • 1
  • M. A. Grechkoseeva
    • 1
  • V. D. Mazurov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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