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

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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 = 2k.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. V. Vasil’ev & M. A. Grechkoseeva

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    I. B. Gorshkov & A. M. Staroletov

  3. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    A. S. Kondrat’ev

Authors
  1. A. V. Vasil’ev
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  2. I. B. Gorshkov
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  3. M. A. Grechkoseeva
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  4. A. S. Kondrat’ev
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  5. A. M. Staroletov
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Correspondence to A. V. Vasil’ev.

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Original Russian Text © A.V. Vasil’ev, I.B.Gorshkov, M.A.Grechkoseeva, A.S.Kondrat’ev, A.M. Staroletov, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 2.

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Vasil’ev, A.V., Gorshkov, I.B., Grechkoseeva, M.A. et al. On recognizability by spectrum of finite simple groups of types B n , C n , and 2 D n for n = 2k . Proc. Steklov Inst. Math. 267 (Suppl 1), 218–233 (2009). https://doi.org/10.1134/S0081543809070207

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  • DOI: https://doi.org/10.1134/S0081543809070207

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