Abstract
In the paper, the ranks, degrees, subdegrees, and double centralizers of permutation representations of the bounded groups2 F 4(q) and3 D 4(q 3) with respect to parabolic maximal subgroups of nonminimal index are found.
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A. S. Kondrat’ev, “Subgroups of finite Chevalley groups,”Uspekhi Mat. Nauk [Russian Math. Surveys],41, No. 1 (247), 57–96 (1986).
B. N. Cooperstein, “Minimal degree for a permutation representation of a classical group,”Israel J. Math.,30, No. 3, 213–235 (1978).
M. W. Liebeck and J. Saxl, “On the orders of maximal subgroups of the finite exceptional groups of Lie type,”Proc. London Math. Soc.,55, 299–330 (1987).
A. V. Vasil’ev, “Minimal permutation representations of finite simple exceptional groups of twisted type,”Algebra i Logika [Algebra and Logic],37, No. 1, 17–35 (1998).
R. W. Carter,Simple Groups of Life Type, Wiley, London (1972).
R. Ree, “A family of simple groups associated with the simple Lie algebra of type (F 4),”Amer. J. Math.,83, 401–420 (1961).
K. Shinoda, “A characterization of odd order extension of Ree groups2 F 4(q),”J. Fac. Sci. Univ. Tokyo,22, 79–102 (1975).
R. Steinberg,Lectures on Chevalley Groups, Yale Univ. Math. Dept. (1968).
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Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 69–76, January, 2000.
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Korableva, V.V. Parabolic permutation representations of the groups2 F 4(q) and3 D 4(q 3). Math Notes 67, 55–60 (2000). https://doi.org/10.1007/BF02675792
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DOI: https://doi.org/10.1007/BF02675792