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Almost Recognizability by Spectrum of Simple Exceptional Groups of Lie Type

Algebra and Logic Aims and scope

The spectrum of a finite group is the set of its elements orders. Groups are said to be isospectral if their spectra coincide. For every finite simple exceptional group L = E 7(q), we prove that each finite group isospectral to L is isomorphic to a group G squeezed between L and its automorphism group, i.e., L ≤ G ≤ AutL; in particular, up to isomorphism, there are only finitely many such groups. This assertion, together with a series of previously obtained results, implies that the same is true for every finite simple exceptional group except the group 3 D 4(2).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. V. Vasil’ev & A. M. Staroletov

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

    A. V. Vasil’ev & A. M. Staroletov

Authors
  1. A. V. Vasil’ev
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  2. A. M. Staroletov
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Correspondence to A. V. Vasil’ev or A. M. Staroletov.

Additional information

Supported by RFBR, grant No. 13-01-00505 (A. V. Vasil’ev).

Supported by RFBR, grant No. 12-01-31221 (A. M. Staroletov).

Translated from Algebra i Logika, Vol. 53, No. 6, pp. 669–692, November-December, 2014.

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Vasil’ev, A.V., Staroletov, A.M. Almost Recognizability by Spectrum of Simple Exceptional Groups of Lie Type. Algebra Logic 53, 433–449 (2015). https://doi.org/10.1007/s10469-015-9305-1

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  • DOI: https://doi.org/10.1007/s10469-015-9305-1

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