×

Subgroups of split orthogonal groups. (English. Russian original) Zbl 0667.20036

Sib. Math. J. 29, No. 3, 341-352 (1988); translation from Sib. Mat. Zh. 29, No. 3(169), 12-25 (1988).
See the review in Zbl 0647.20043.

MSC:

20G15 Linear algebraic groups over arbitrary fields
20E15 Chains and lattices of subgroups, subnormal subgroups
20E07 Subgroup theorems; subgroup growth

Citations:

Zbl 0647.20043
PDFBibTeX XMLCite
Full Text: DOI

References:

[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). · Zbl 0461.20027
[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). · Zbl 0444.20039
[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). · Zbl 0461.20037
[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).
[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). · Zbl 0529.20029
[6] N. A. Vavilov, ?Bruhat decomposition of one-dimensional transformations,? Vestn. Leningr. Gos. Univ., Ser. 1, No. 3, 14-20 (1986).
[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). · Zbl 0529.20036
[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). · Zbl 0476.20030
[9] G. M. Seitz, ?Subgroups of finite groups of Lie type,? J. Algebra,61, No. 1, 16-27 (1979). · Zbl 0426.20036 · doi:10.1016/0021-8693(79)90302-8
[10] Z. I. Borevich, ?On parabolic subgroups in linear groups over a semilocal ring,? Vestn. Leningr. Gos. Univ., No. 13, 16-24 (1976). · Zbl 0389.20033
[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).
[12] N. A. Vavilov and E. B. Plotkin, ?Net subgroups of Chevalley groups,? J. Sov. Math.,19, No. 1 (1982);27, No. 4 (1984). · Zbl 0485.20037
[13] K. Suzuki, ?On parabolic subgroups of Chevalley groups over local rings,? Tohoku Math. J.,28, No. 1, 57-66 (1976). · Zbl 0357.22005 · doi:10.2748/tmj/1178240878
[14] N. A. Vavilov, ?On parabolic subgroups of Chevalley groups over a semilocal ring,? J. Sov. Math.,37, No. 2 (1987). · Zbl 0612.20028
[15] V. A. Koibaev, ?Examples of nonmonomial linear groups without transvections,? J. Sov. Math.,20, No. 6 (1982). · Zbl 0497.20034
[16] A. Borel and J. Tits, ?Reductive groups,? Matematika: Sb. perevodov,11, No. 1, 43-111; No. 2, 3-31 (1967).
[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.
[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).
[19] O. King, ?On subgroups of the special linear group containing the special orthogonal group,? J. Algebra,96, No. 1, 178-193 (1985). · Zbl 0572.20028 · doi:10.1016/0021-8693(85)90045-6
[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). · Zbl 0461.20033
[21] E. V. Dybkova, ?Index of a net subgroup in a symplectic group over a Dedekind ring,? J. Sov. Math.,37, No. 2 (1987). · Zbl 0612.20029
[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). · Zbl 0449.20049 · doi:10.1016/0021-8693(81)90288-X
[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). · Zbl 0467.20037 · doi:10.1016/0021-8693(81)90327-6
[25] O. King, ?Maximal subgroups of the orthogonal group over a field of characteristic two,? J. Algebra,76, No. 2, 540-548 (1982). · Zbl 0486.20029 · doi:10.1016/0021-8693(82)90231-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.