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Almost recognizability by spectrum of finite simple linear groups of prime dimension

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Abstract

The spectrum of a group is the set of its element orders. Let L = PSL n (q), where n is a prime greater than 3. We show that every finite group whose spectrum is the same as the spectrum of L is isomorphic to an extension of L by a subgroup of the outer automorphism group of L.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. A. Grechkoseeva

  2. Novosibirsk State University, Novosibirsk, Russia

    D. V. Lytkin

Authors
  1. M. A. Grechkoseeva
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  2. D. V. Lytkin
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Corresponding author

Correspondence to M. A. Grechkoseeva.

Additional information

Original Russian Text Copyright © Grechkoseeva M.A. and Lytkin D.V.

The authors were supported by the Russian Foundation for Basic Research (Grant 11-01-91158), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grants NSh-3669.2010.1 and MK-2136.2010.1), and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1.10726).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 805–818, July–August, 2012.

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Grechkoseeva, M.A., Lytkin, D.V. Almost recognizability by spectrum of finite simple linear groups of prime dimension. Sib Math J 53, 645–655 (2012). https://doi.org/10.1134/S0037446612040076

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  • DOI: https://doi.org/10.1134/S0037446612040076

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