Geodesic
Classification of the maximal arithmetic subgroups of indefinite orthogonal groups of type $(B_l)$
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 71-89 
A. A. Bondarenko. Classification of the maximal arithmetic subgroups of indefinite orthogonal groups of type $(B_l)$. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 71-89. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An explicit classification is obtained for the maximal arithmetic subgroups of indefinite orthogonal $K$-groups of type $(B_l)$, where $K$ is a global field $(\operatorname{char}K\ne2)$. As a preliminary, a local analogue of the maximality problem is considered, and conditions are determined under which, for groups of the type indicated, local maximality implies global. Bibliography: 14 titles.

[1] Algebraicheskaya teoriya chisel, Mir, M., 1969 | MR

[2] Bondarenko A. A., “K probleme maksimalnosti arifmeticheskikh podgrupp v ortogonalnykh gruppakh tipa $B_n$”, Matem. zametki, 16:1 (1974), 151–161 | MR | Zbl

[3] Bondarenko A. A., “K klassifikatsii maksimalnykh arifmeticheskikh podgrupp v razlozhimykh gruppakh”, Matem. sb., 102(144) (1977), 155–172 | MR | Zbl

[4] Bondarenko A. A., “Maksimalnye arifmeticheskie podgruppy neopredelennykh ortogonalnykh grupp tipa $(B_l)$”, Vsesoyuznyi simp. po teorii grupp (tezisy dokl.), Kiev, 1982, 15–16

[5] Veil A., Osnovy teorii chisel, Mir, M., 1972 | MR

[6] Dedonne Zh., Geometriya klassicheskikh grupp, Mir, M., 1974 | MR

[7] Platonov V. P., “Problema silnoi approksimatsii i gipoteza Knezera–Titsa dlya algebraicheskikh grupp”, Izv. AN SSSR. Ser. matem., 33 (1969), 1211–1219 | MR | Zbl

[8] Platonov V. P., “Dopolnenie k rabote “Problema silnoi approksimatsii i gipoteza Knezera–Titsa dlya algebraicheskikh grupp””, Izv. AN SSSR. Ser. matem., 34 (1970), 775–777 | MR | Zbl

[9] Platonov V. P., “K probleme maksimalnosti arifmeticheskikh grupp”, DAN SSSR, 200:3 (1971), 530–533 | MR | Zbl

[10] Platonov V. P., “Arifmeticheskaya teoriya algebraicheskikh grupp”, UMN, 37:3 (1982), 3–54 | MR | Zbl

[11] Bruhat F., “Sous-groupes compacts maximaux des groupes semisimles $p$-adiques”, Seminaire Bourbaki, 1963/1964, no. 271, 271-01–271-10

[12] Bruhat F., “$\mathfrak{P}$-adic groups”, Algebraic Groups and Discontinuous Subgroups (Amer. Math. Soc), 1966, 63–70 | MR | Zbl

[13] Bruhat F., Tits J., “Groupes reductifs sur un corps local”, Publ. Math: I.H.E.S., 1972, no. 41, 5–252 | MR

[14] O'Meara O. T., Introduction to quadratic forms, Springer, Berlin–Heidelberg–New York, 1963 | Zbl