On the lattice of subgroups of chevalley groups containing a split maximal torus

Bibliography

• Aschbacher , M. 1984 . On the maximal subgroups of the finite classical groups . Invent. Math , 76 ( 3 ) : 469 – 514 .
   Web of Science ®Google Scholar
• Berman , S. and Moody , R. 1975 . Extensions of Chevalley groups . Israel J. Math , 22 ( 3 ) : 42 – 51 .
   Google Scholar
• Borel , A. 1969 . Linear algebraic groups , 398 – 398 . Amsterdam, New York : Benjamin .
   Google Scholar
• Borel , A. 1970 . Properties and linear representations of Chevalley groups . Lecture Notes Math , 131
   Google Scholar
• Borel , A. 1949 . de Siebenthal J. Les sous-groupes fermés connexes de rang maximal des groupes de Lie clos . Comm. Math. Heiv , 23 ( 2 ) : 200 – 221 .
   Google Scholar
• Borel , A. 1965 . Tits J. Groupes réductifs . Pubî. Math. Inst. Hautes Et. Sei , 27 ( 2 ) : 55 – 150 .
   Google Scholar
• Borel , A. 1971 . Tits J. Elements unipotents et sous-groupes paraboliques de groupes réductifs. I . Invent. Math , 12 ( 2 ) : 97 – 104 .
   Google Scholar
• Borewicz , Z.I. 1981 . Description of subgroups of the general linear group that contain the group of diagonal matrices . J. Sov Math , 17 ( 2 ) : 1718 – 1730 .
   Google Scholar
• Borewicz , Z.I. 1982 . Some subgroups of the general linear group . J. Sov Math , 20 ( 6 ) : 2528 – 2532 .
   Google Scholar
• Borewicz , Z.I. 1981 . On the arrangement of subgroups . J. Sov. Math , 19 ( 6 ) : 977 – 981 .
   Google Scholar
• Borewicz , Z.I. and Koibaev , V.A. 1978 . “ Subgroups of the general linear group over the field of five elements ” . In Algebra and Number Theory , Vol. 3 , 9 – 32 . Ordzhonikidze (Vladikavkaz) . (in Russian)
   Google Scholar
• Borewicz , Z.I. and Vavilov , N.A. 1980 . Subgroups of the general linear group over a semilocal ring containing the group of diagonal matrices . Proc. Steklov Inst. Math , 3 : 41 – 54 .
   Google Scholar
• Bourbaki , N. 1968 . Groupes et algèbres de Lie , Vol. 4-6 , 4 – 6 . Pans : Hermann .
   Google Scholar
• Carter , R.W. 1970 . Conjugacy classes in the Weyl group . Lecture Notes Math , 131 : 297 – 318 .
   Google Scholar
• Carter , R.W. 1972 . Simple groups of Lie type , 331 – 331 . London et al : Wiley .
   Google Scholar
• Carter , R.W. 1972 . Conjugacy classes in the Weyl group . Compositio Math , 25
   Google Scholar
• Carter , R.W. 1985 . Finite groups of Lie type: Conjugacy classes and complex characters , 544 – 544 . London : Wiley . et al
   Google Scholar
• Deriziotis , D.I. 1977 . Semi-simple conjugacy classes of Chevailey groups , Univ of Warwick . Ph. D. Thesis
   Google Scholar
• Deriziotis , D.I. 1981 . Centralizers of semi-simple elements in a Chevailey group . Comm. Algebra , 9 ( 19 ) : 1997 – 2014 .
   Web of Science ®Google Scholar
• Dybkova , E.V. Arrangement of subgroups in symplectic groups , Vol. 986 , 145 – 145 . Leningrad State Univ . Ph. D Thesis,, (in Russian)
   Google Scholar
• Dye , R.W. 1985 . Maximal subgroups of the finite orthogonal and unitary groups stabilizing anisotropic subspaces . Math. Z , 189 : 111 – 129 .
   Google Scholar
• Dynkin , E.B. 1957 . Semi-simple subalgebras of semi-simple Lie algebras . Amer. Math. Soc. Transi Ser , 6 : 111 – 244 .
   Google Scholar
• Friedland , S. 1985 . Maximality of the monomial subgroup . Linear Multilinear Algebra , 18
   Google Scholar
• Golubitsky , M. 1972 . Primitive actions and maximal subgroups of Lie groups . J. Diff. Geom , 7 : 175 – 191 .
   Google Scholar
• Golubitsky , M. 1971 . Rothschild B. Primitive subalgebras of exceptional Lie algebras . Bull. Amer. Math. Soc , 77 ( 6 ) : 983 – 986 .
   Google Scholar
• Golubitsky , M. and Rothschild , B. 1971 . Primitive subalgebras of exceptional Lie algebras . Pacif J. Math , 39 ( 2 ) : 371 – 393 .
   Google Scholar
• Goto , M. and Grosshans , F.D. 1978 . Semi-simple Lie algebras , 480 – 480 . Basel, New York : Marcel Dekker .
   Google Scholar
• Howlett , R.B. 1980 . Normalizers of parabolic subgroups of reflection groups . J. London Math. Soc , 21 : 62 – 80 .
   Google Scholar
• Humphreys , J.E. 1975 . Linear algebraic groups , 247 – 247 . New York : Springer . et al
   Google Scholar
• Humphreys , J.E. 1980 . Introduction to Lie algebras and representation theory, 3rd Printing , 171 – 171 . New York et al : Springer .
   Google Scholar
• Idowu , A.J. and Morris , A.O. 1987 . Some combinatorial results for Weyl groups . Math. Proc. Cambridge Phil. Soc , 101 : 405 – 420 .
   Google Scholar
• Key , J.D. 1975 . Some maximal subgroups of PSL(n,<y), n > 3, q = 2r . Geom. Dedic , 4 : 377 – 386 . erratum - ibid. - 1977. - V.6, N.3. - P.389
   Google Scholar
• Key , J.D. 1979 . Sone maximal subgroups of certain projective unimodular groups . J. London Math. Soc , 19 ( 2 ) : 219 – 230 .
   Google Scholar
• King , O.H. 1981 . On some maximal subgroups of the classical groups . J. Algebra , 68 ( 2 ) : 109 – 120 .
   Google Scholar
• King , O.H. 1981 . Maximal subgroups of the classical groups associated with nonisotropic subspaces of a vector space . J. Algebra , 73 ( 2 ) : 350 – 375 .
   Web of Science ®Google Scholar
• King , O.H. 1982 . Maximal subgroups of the orthogonal group over a field of characteristic two . J. Algebra , 76 ( 3 ) : 540 – 548 .
   Google Scholar
• King , O.H. 1982 . Imprimitive maximal subgroups of the general linear, special linear, symplectic and general symplectic groups . J. London Math. Soc , 25 ( 3 ) : 416 – 424 .
   Google Scholar
• King , O.H. 1983 . Imprimitive maximal subgroups of the orthogonal, special orthogonal, unitary and special unitary groups . Math. Z , 182 ( 3 ) : 193 – 203 .
   Google Scholar
• King , O.H. 1984 . Imprimitive maximal subgroups of the symplectic, orthogonal and unitary groups . Geom. Dedic , 15 ( 3 ) : 339 – 353 .
   Google Scholar
• King , O.H. 1985 . On subgroups of the special linear group containing the special orthogonal group . J. Algebra , 96 ( 3 ) : 178 – 193 .
   Google Scholar
• King , O.H. 1990 . On subgroups of the special linear group containing the diagonal subgroup . J. Algebra , 132 ( 3 ) : 198 – 204 .
   Google Scholar
• Kleidman , P. and Liebeck , M. 1990 . The subgroup structure of the unite classical groups , 303 – 303 . Cambridge Univ. Press .
   Google Scholar
• Koibaev , V.A. 1982 . Some examples of non-monomial linear groups without transvections . J. Sov Math , 20 ( 6 ) : 2610 – 2611 .
   Google Scholar
• Koibaev , V.A. 1979 . “ Subgroups of the full linear group over the field of four elements ” . In Algebra and Number Theory 21 – 31 . Nalchik (in Russian)
   Google Scholar
• Koibaev , V.A. 1981 . “ Subgroups of the full linear group over the field of three elements ” . In Structural Properties of Algebraic Systems 56 – 68 . Nalchik (inRussian)
   Google Scholar
• Kondratiev , A.S. 1986 . Subgroups of finite Chevalley groups . Russian Math. Surv , 41 : 65 – 118 .
   Google Scholar
• Zhi , Li Shang . 1987 . Maximal subgroups m classical groups over arbitrary fields . Proc. Symp. Pure Math , 47 : 487 – 493 . Part (2)
   Google Scholar
• Shang Zhi , Li . 1989 . The maximality of monomial subgroups of linear groups over division rings . J. Algebra , 127 ( 1 ) : 22 – 39 .
   Web of Science ®Google Scholar
• Manin , Yu.I . 1974 . Cubic forms: algebra, geometry, arithmetic , 292 – 292 . Amsterdam : North Holland . London
   Google Scholar
• Pierce , S. 1981 . Maximal subgroups of the orthogonal groups . J. Geom , 16 : 30 – 40 .
   Google Scholar
• Seitz , G.M. 1979 . Subgroups of finite groups of Lie type.” -“J. Algebra , 61 : 16 – 27 .
   Web of Science ®Google Scholar
• Seitz , G.M. 1980 . Properties of the known simple groups . Proc. Symp. Pure. Math , 37 : 231 – 237 .
   Google Scholar
• Seitz , G.M. 1982 . On the subgroup structure of classical groups . Comm. Algebra , 10 ( 8 ) : 875 – 885 .
   Web of Science ®Google Scholar
• Seitz , G.M. 1983 . Root subgroups for maximal tori in finite groups of Lie type . Pacif. J. Math , 106 ( 8 ) : 153 – 244 .
   Google Scholar
• Seligman , G.B. 1967 . Modular Lie algebras , 165 – 165 . Berlin : Springer . et al
   Google Scholar
• Semenov , A.A. 1991 . Bruhat decomposition of semi-simple long root tori in Chevalley groups , 143 – 143 . Leningrad State Univ . Ph.D. Thesis, (in Russian)
   Google Scholar
• Springer , T.A. 1981 . Linear algebraic groups , 320 – 320 . Boston : Birkhäuser: . et al
   Google Scholar
• Steinberg , R. 1968 . Lectures on Chevalley groups , 277 – 277 . Yale University .
   Google Scholar
• Tits , J. Sous-algèbres des algÈbres de Lie semi-simples . SÉminaire Bourbaki, 7eme annÉe /1955 . 1954 . Edited by: Morozov , V. D’après , Mal-Cev , A. Karpelevich , F. Vol. 119 , pp. 1 – 18 . Paris -Expose
   Google Scholar
• Tits , J. 1962 . “ Groupes semi-simples isotropes ” . In Colloq. Théorie des groupes algébriques (Bruxelles, 1962) 137 – 147 . Paris
   Google Scholar
• Dao Ron , Ton . 1987 . A class of maximal subgroups in finite classical groups . J. Algebra , 106 ( 2 ) : 536 – 542 .
   Web of Science ®Google Scholar
• Dao Ron , Ton . 1987 . Second class of maximal subgroups in finite classical groups . J. Algebra , 108 ( 2 ) : 578 – 588 .
   Web of Science ®Google Scholar
• Vavilov , N.A. 1981 . On subgroups of the general linear group over a semi-local ring that contain the group of diagonal matrices . Vestnik Leningr. Univ., Math , 14 ( 2 ) : 9 – 15 .
   Google Scholar
• Vavilov , N.A. 1981 . On subgroups of split orthogonal groups in even dimensions . Bull. Acad. Polon. Sei , 29 ( 2 ) : 425 – 429 . Ser. Sei. Math
   Google Scholar
• Vavilov , N.A. 1984 . Bruhat decomposition for subgroups containing the group of diagonal matrices. I, II . J. Sov. Math , 24 ( 1984 ) : 399 – 406 . V. 27 -P.2865-2874
   Google Scholar
• Vavilov , N.A. 1985 . On subgroups of the special linear group that contain the group of diagonal matrices. I, II, III, IV . Vestnik Leningr. Univ., Math. , 18 ( 4 ) : 3 – 7 . 1986. - V.19. -P.9-15; 1987. - V.20. -P.l-8; 1988. - N.3. - P.7-15
   Google Scholar
• Vavilov , N.A. 1991 . Maximal subgroups of Chevalley groups containing a split maximal torus . Transi Amer. Math. Soc , 149 ( 4 ) : 53 – 59 . 2nd Ser
   Google Scholar
• Vavilov , N.A. 1986 . Bruhat decomposition of one-dimensional transformations . Vestnik Leningr. Univ., Math , 19 ( 4 ) : 17 – 24 .
   Google Scholar
• Vavilov , N.A. 1987 . A conjugacy theorem for subgroups of GLn containing the group of diagonal matrices . Colloq. Math , 54 ( 4 ) : 9 – 14 .
   Google Scholar
• Vavilov , N.A. 1987 . Subgroups of split classical groups , 334 – 334 . Leningrad State Univ . Dr. Sei. thesis (Habilitationsschrift),, (in Russian)
   Google Scholar
• Vavilov , N.A. 1988 . Weight elements of Chevalley groups . Soviet Math. Doki , 37 : 92 – 95 .
   Google Scholar
• Vavilov , N.A. 1988 . Conjugacy theorems for subgroups of extended Chevalley groups containing a split maximal torus . Sovjet Math. Dokl , 37 ( 2 ) : 360 – 363 .
   Google Scholar
• Vavilov , N.A. 1988 . On subgroups of split orthogonal groups. I, II . Siberian Math. J , 29 ( 3 ) : 341 – 352 . ibid, submitted
   Web of Science ®Google Scholar
• Vavilov , N.A. 1988 . “ Bruhat decomposition of the semisimple long root elements m Chevalley groups ” . In Rings and modules. Limit theorems of probability theory , 18 – 39 . IL : Leningrad Univ. Press . (in Russian, English transi, in Transi. Amer. Math. Soc, 2nd Ser.)
   Google Scholar
• Vavilov , N.A. 1989 . Semisimple root elements and triples of unipotent root subgroups m a Chevalley group . Problems in Algebra (Minsk) , 4 : 162 – 173 . (in Russian)
   Google Scholar
• Vavilov , N.A. 1991 . On subgroups of the split classical groups . Proc. Math. Inst. Steklov , 4 : 27 – 41 .
   Google Scholar
• Vavilov , N.A. 1993 . Subgroups of Chevalley groups containing a maximal torus . Transi. Amer. Math. Soc , 155 : 59 – 100 . 2nd ser
   Google Scholar
• Vavilov , N.A. 1993 . On subgroups of the spinorial group containing a split maximal torus. I, II . J. Sov Math , 63 ( 6 ) : 638 – 653 .
   Google Scholar
• Vavilov , N.A. Structure of Chevalley groups over commutative rings . Proc Conf. Non-associative algebras and related topics, (Hiroshima - ) . 1990 . pp. 219 – 335 . London : World Sei. Publ . et al
   Google Scholar
• Vavilov , N.A. 1993 . Unipotent elements in subgroups of extended Chevalley groups containing a split maximal torus . Russian Math. Doklady , 328 ( 5 ) : 112 – 115 .
   Google Scholar
• Vavilov , N.A. 1995 . “ Intermediate subgroups in Chevalley groups ” . In Groups of Lie Type and their Geometries (Como - 1993) , 233 – 280 . Cambridge Univ. Press .
   Google Scholar
• Vavilov , N.A. and Dybkova , E.V. 1984 . Subgroups of the general symplectic group containing the group of diagonal matrices. I, II . J. Sov. Math , 24 : 406 – 416 . 1985. - V.30. - P.1823-1832
   Google Scholar
• Vavilov , N.A. and Semenov , A.A. 1994 . Semi-simple root elements of Chevalley groups . Russian Math. Doklady , 338 ( 6 ) : 725 – 728 .
   Google Scholar
• Wallach , N. 1968 . On maximal subsystems of root systems . Canad. J. Math , 20 ( 3 ) : 555 – 574 .
   Google Scholar
• Zalesskii , A.E. 1985 . Linear groups . J. Sov. Math , 31 ( 3 ) : 2974 – 3004 .
   Google Scholar