Abstract
The minimal degree for a permutation representation of the finite linear groups, and finite classical groups is determined.
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M. Aschbacher and G. Seitz.Involutions in chevalley groups over fields of even order, to appear.
B. Cooperstein,Some geometries associated with parabolic representations of groups of Lie type, Canad. J. Math.27 (1976), 1021–1031.
L. E. Dickson,Determination of all subgroups of the known simple group of order 25920, Trans. Amer. Math. Soc.5 (1904), 126–166.
L. E. Dickson,Linear Groups With an Exposition of Galois Field Theory, reprint of 1901 ed., Dover, New York, 1958.
D. E. Flesner,Maximal subgroups of PSp 4(2n) containing central elations or noncentral skew elations, to appear in Illnois J. Math.
D. Gorenstein,Finite Groups, Harper and Row, New York, 1968.
R. W. Hartley,Determination of the ternary collineation groups whose coefficients lie in GF(2n), Ann. of Math.27 (1925), 140–158.
W. Huppert,Endliche Gruppen, Vol. 1, Springer Verlag, Berlin, 1967.
W. M. Kantor,Subgroups of classical groups generated by long root elements, unpublished.
J. E. McLaughlin,Course Notes on Cohomology of Linear and Classical Groups, unpublished.
J. E. McLaughlin,Some groups generated by transvections, Arch. Math. Basel18 (1967), 364–368.
J. E. McLaughlin,Some subgroups of SL n (F 2), Illinois J. Math.13 (1969), 108–115.
M. H. Mitchell,Determination of the ordinary and modular ternary lineary groups, Trans. Amer. Math. Soc.12 (1911), 207–242.
H. H. Mitchell,The subgroups of the quaternary Abelian linear group, Trans. Amer. Math. Soc.15 (1914), 379–396.
W. Patton, Ph.D. Thesis, 1971.
G. M. Seitz,Flag transitive subgroups of Chevalley groups, Ann. of Math.97 (1973), 27–56.
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Supported in part by NSF MCS 76-07035.
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Cooperstein, B.N. Minimal degree for a permutation representation of a classical group. Israel J. Math. 30, 213–235 (1978). https://doi.org/10.1007/BF02761072
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DOI: https://doi.org/10.1007/BF02761072