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On recognition of finite simple groups with connected prime graph

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Abstract

The spectrum of a finite group is the set of its element orders. We prove a theorem on the structure of a finite group whose spectrum is equal to the spectrum of a finite nonabelian simple group. The theorem can be applied to solving the problem of recognizability of finite simple groups by spectrum.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. V. Vasil’ev

  2. Novosibirsk State University, Novosibirsk, Russia

    I. B. Gorshkov

Authors
  1. A. V. Vasil’ev
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  2. I. B. Gorshkov
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Corresponding author

Correspondence to A. V. Vasil’ev.

Additional information

Original Russian Text Copyright © 2009 Vasil’ev A. V. and Gorshkov I. B.

The authors were supported by the Russian Foundation for Basic Research (Grants 08-01-00322 and 06-01-39001), the Siberian Division of the Russian Academy of Sciences (Integration Project No. 2006.1.2), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1), and a grant of the President of the Russian Federation for Young Science Doctors (Grant MD-2848.2007.1).

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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 292–299, March–April, 2009.

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Vasil’ev, A.V., Gorshkov, I.B. On recognition of finite simple groups with connected prime graph. Sib Math J 50, 233–238 (2009). https://doi.org/10.1007/s11202-009-0027-2

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  • DOI: https://doi.org/10.1007/s11202-009-0027-2

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