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On finite groups isospectral to simple symplectic and orthogonal groups

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Abstract

The spectrum of a finite group is the set of its element orders. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field of an arbitrary positive characteristic p. It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over a field of the same characteristic p.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

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

Authors
  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

Original Russian Text Copyright © 2009 Vasil’ev A. V., Grechkoseeva M. A., and Mazurov V. D.

The authors were supported by the Russian Foundation for Basic Research (Grant 08-01-00322), the President of the Russian Federation (Grants NSh-344.2008.1 and MK-377.2008.1), and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1.419).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1225–1247, November–December,2009.

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Vasil’ev, A.V., Grechkoseeva, M.A. & Mazurov, V.D. On finite groups isospectral to simple symplectic and orthogonal groups. Sib Math J 50, 965–981 (2009). https://doi.org/10.1007/s11202-009-0107-3

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  • DOI: https://doi.org/10.1007/s11202-009-0107-3

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