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Characterization of the finite simple groups by spectrum and order

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Algebra and Logic Aims and scope

We give an affirmative answer to Question 12.39 in the Kourovka Notebook. Namely, it is proved that a finite simple group and a finite group having equal orders and same sets of element orders are isomorphic.

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Authors and Affiliations

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

    A. V. Vasil’ev, M. A. Grechkoseeva & V. D. Mazurov

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

    A. V. Vasil’ev, M. A. Grechkoseeva & V. D. Mazurov

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  1. A. V. Vasil’ev
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  2. M. A. Grechkoseeva
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  3. V. D. Mazurov
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Correspondence to A. V. Vasil’ev.

Additional information

Supported by RFBR (project No. 08-01-00332), by the Council for Grants (under RF President) (grants NSh-334.2008.1 and MK-377.2008.1), by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.419), and by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” in 2009-2013 (gov. contract No. 02.740.11.0429).

Translated from Algebra i Logika, Vol. 48, No. 6, pp. 685-728, November-December, 2009.

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Vasil’ev, A.V., Grechkoseeva, M.A. & Mazurov, V.D. Characterization of the finite simple groups by spectrum and order. Algebra Logic 48, 385–409 (2009). https://doi.org/10.1007/s10469-009-9074-9

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  • DOI: https://doi.org/10.1007/s10469-009-9074-9

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