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Subgroups of split orthogonal groups

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Literature Cited

  1. Z. I. Borevich, “Description of the subgroups of the general linear group containing the group of diagonal matrices,” J. Sov. Math.,17, No. 2 (1981).

  2. Z. I. Borevich and N. A. Vavilov, “Subgroups of the general linear group over a semilocal ring, containing the group of diagonal matrices,” Trudy Mat. Inst. Steklov, Akad. Nauk SSSR,148, 43–57 (1978).

    Google Scholar 

  3. N. A. Vavilov, “On subgroups of the general linear group over a semilocal ring, containing the group of diagonal matrices,” Vestn. Leningr. Gos. Univ., No. 1, 10–15 (1981).

    Google Scholar 

  4. N. A. Vavilov, “On conjugacy of subgroups of the general linear group containing the group of diagonal matrices,” Usp. Mat. Nauk,34, No. 5, 216–217 (1979).

    Google Scholar 

  5. N. A. Vavilov, “The Bruhat decomposition for subgroups containing the group of diagonal matrices,” J. Sov. Math.,24, No. 4 (1984);27, No. 4 (1984).

  6. N. A. Vavilov, “Bruhat decomposition of one-dimensional transformations,” Vestn. Leningr. Gos. Univ., Ser. 1, No. 3, 14–20 (1986).

    Google Scholar 

  7. N. A. Vavilov and E. V. Dybkova, “Subgroups of the general symplectic group containing the group of diagonal matrices,” J. Sov. Math.,24, No. 4 (1984);30, No. 1 (1985).

  8. N. A. Vavilov, “Subgroups of split orthogonal groups in even dimensions,” Bull. Acad. Polon. Sci. Ser. Sci. Math.,29, Nos. 9/10, 425–429 (1981).

    Google Scholar 

  9. G. M. Seitz, “Subgroups of finite groups of Lie type,” J. Algebra,61, No. 1, 16–27 (1979).

    Google Scholar 

  10. Z. I. Borevich, “On parabolic subgroups in linear groups over a semilocal ring,” Vestn. Leningr. Gos. Univ., No. 13, 16–24 (1976).

    Google Scholar 

  11. Z. I. Borevich and N. A. Vavilov, “Distribution of subgroups in the general linear group over a commutative ring,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,165, 24–42 (1984).

    Google Scholar 

  12. N. A. Vavilov and E. B. Plotkin, “Net subgroups of Chevalley groups,” J. Sov. Math.,19, No. 1 (1982);27, No. 4 (1984).

  13. K. Suzuki, “On parabolic subgroups of Chevalley groups over local rings,” Tohoku Math. J.,28, No. 1, 57–66 (1976).

    Google Scholar 

  14. N. A. Vavilov, “On parabolic subgroups of Chevalley groups over a semilocal ring,” J. Sov. Math.,37, No. 2 (1987).

  15. V. A. Koibaev, “Examples of nonmonomial linear groups without transvections,” J. Sov. Math.,20, No. 6 (1982).

  16. A. Borel and J. Tits, “Reductive groups,” Matematika: Sb. perevodov,11, No. 1, 43–111; No. 2, 3–31 (1967).

    Google Scholar 

  17. N. A. Vavilov, “On subgroups of the extended Chevalley groups containing a maximal torus,” 16th All-Union Algebra Conference. Abstracts of Lectures, Vol. I, LOMI, Leningrad (1981), pp. 26, 27.

    Google Scholar 

  18. N. A. Vavilov, “On subgroups of the special linear group containing the group of diagonal matrices,” Vestn. Leningr. Gos. Univ., No. 22, 3–7 (1985); ibid. N. A. Vavilov, “On subgroups of the special linear group containing the group of diagonal matrices, ”Vestn. Leningr. Gos. Univ., Ser. 1, No. 2, 10–15 (1986).

    Google Scholar 

  19. O. King, “On subgroups of the special linear group containing the special orthogonal group,” J. Algebra,96, No. 1, 178–193 (1985).

    Google Scholar 

  20. Z. I. Borevich, E. V. Dybkova, and L. Yu. Kolotilina, “On conjugacy of net subgroups in linear groups,” J. Sov. Math.,17, No. 4 (1981).

  21. E. V. Dybkova, “Index of a net subgroup in a symplectic group over a Dedekind ring,” J. Sov. Math.,37, No. 2 (1987).

  22. N. A. Vavilov, “Maximal subgroups of Chevalley groups, containing a maximal split torus,” in: Rings and Modules. Limit Theorems of Probability Theory, Part I [in Russian], Leningrad State Univ. (1986), pp. 67–75.

  23. O. King, “On some maximal subgroups of the classical groups,” J. Algebra,68, No. 1, 109–120 (1981).

    Google Scholar 

  24. O. King, “Maximal subgroups of the classical groups associated with nonisotropic subspaces of a vector space,” J. Algebra,73, No. 2, 350–375 (1981).

    Google Scholar 

  25. O. King, “Maximal subgroups of the orthogonal group over a field of characteristic two,” J. Algebra,76, No. 2, 540–548 (1982).

    Google Scholar 

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Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 12–25, May–June, 1988.

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Vavilov, N.A. Subgroups of split orthogonal groups. Sib Math J 29, 341–352 (1988). https://doi.org/10.1007/BF00969641

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  • DOI: https://doi.org/10.1007/BF00969641

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