Abstract
Let L be a simple linear or unitary group of dimension larger than 3 over a finite field of characteristic p. We deal with the class of finite groups isospectral to L. It is known that a group of this class has a unique nonabelian composition factor. We prove that if L ≠ U 4(2), U 5(2) then this factor is isomorphic to either L or a group of Lie type over a field of characteristic different from p.
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Original Russian Text Copyright © 2011 Vasil’ ev A. V., Grechkoseeva M. A., and Staroletov A. M.
The authors were supported by the Russian Foundation for Basic Research (Grants 08-01-00322 and 10-01-90007-Bel a), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grants NSh-3669.2010.1 and MK-2136.2010.1), the Program “Development of the Scientific Potential of Higher Education” of the Russian Federal Agency for Education (Grant 2.1.1.419), the Federal Target Program “Scientific and Educational Personnel of Innovation Russia” for 2009–2013 (State Contracts 02.740.11.0429 and 02.740.11.5191), and Lavrent’ev’s Grant for Young Scientists of the Siberian Division of the Russian Academy of Sciences (Resolution No. 43 of 04.02.2010).
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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 1, pp. 39–53, January–February, 2011.
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Vasil’ev, A.V., Grechkoseeva, M.A. & Staroletov, A.M. On finite groups isospectral to simple linear and unitary groups. Sib Math J 52, 30–40 (2011). https://doi.org/10.1134/S0037446606010046
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DOI: https://doi.org/10.1134/S0037446606010046