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Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2

Algebra and Logic Aims and scope

Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group L of dimension n over an arbitrary field of characteristic 2, we prove that any finite group G isospectral to L is isomorphic to an automorphic extension of L. An explicit formula is derived for the number of isomorphism classes of finite groups that are isospectral to L. This account is a continuation of the second author's previous paper where a similar result was established for finite simple linear groups L in a sufficiently large dimension (n > 26), and so here we confine ourselves to groups of dimension at most 26.

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Author information

Authors and Affiliations

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

    A. V. Vasilyev

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

    M. A. Grechkoseeva

Authors
  1. A. V. Vasilyev
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  2. M. A. Grechkoseeva
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Correspondence to A. V. Vasilyev.

Additional information

Supported by RFBR (project Nos. 08-01-00322 and 06-01-39001), by SB RAS (Integration Project No. 2006.1.2), and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1) and Young Doctors and Candidates of Science (grants MD-2848.2007.1 and MK-377.2008.1).

Translated from Algebra i Logika, Vol. 47, No. 5, pp. 558–570, September–October, 2008.

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Vasilyev, A.V., Grechkoseeva, M.A. Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2. Algebra Logic 47, 314–320 (2008). https://doi.org/10.1007/s10469-008-9026-9

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  • DOI: https://doi.org/10.1007/s10469-008-9026-9

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