Geodesic
On the classification of maximal arithmetic subgroups in split groups
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 135-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain an explicit classification of the maximal arithmetic subgroups of the $Q$-split orthogonal groups of type $(D_l)$, where $Q$ is the field of rational numbers or the field of rational functions of one variable with finite field of constants $(\operatorname{char}Q\ne2)$. In view of known results, this completes the explicit classification of maximal arithmetic subgroups for all $Q$-split classical simple groups. As a preliminary, we obtain an explicit solution of a local analogue of the maximality problem for split orthogonal groups of type $(D_l)$ over a non-Archimedean locally compact field of characteristic $\ne2$. Bibliography: 18 titles. 
@article{SM_1977_31_2_a0,
     author = {A. A. Bondarenko},
     title = {On the classification of maximal arithmetic subgroups in split groups},
     journal = {Sbornik. Mathematics},
     pages = {135--150},
     year = {1977},
     volume = {31},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_2_a0/}
}
TY  - JOUR
AU  - A. A. Bondarenko
TI  - On the classification of maximal arithmetic subgroups in split groups
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 135
EP  - 150
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_31_2_a0/
LA  - en
ID  - SM_1977_31_2_a0
ER  - 
%0 Journal Article
%A A. A. Bondarenko
%T On the classification of maximal arithmetic subgroups in split groups
%J Sbornik. Mathematics
%D 1977
%P 135-150
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_31_2_a0/
%G en
%F SM_1977_31_2_a0
A. A. Bondarenko. On the classification of maximal arithmetic subgroups in split groups. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 135-150. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a0/

[1] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, izd-vo «Nauka», Moskva, 1972 | MR

[2] L. A. Gutnik, I. I. Pyatetskii-Shapiro, “Maksimalnye diskretnye podgruppy unimodulyarnoi gruppy”, Trudy mosk. matem. ob-va, XV (1966), 279–295 | MR

[3] N. Dzhekobson, Teoriya kolets, IL, Moskva, 1947

[4] Zh. Dedonne, Geometriya klassicheskikh grupp, izd-vo «Mir», Moskva, 1974 | MR

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

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

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

[8] V. P. Platonov, “Algebraicheskie gruppy”, Algebra. Topologiya. Geometriya, 11, 1974, 5–36 | MR | Zbl

[9] N. D. Allan, “The problem of the maximality of arithmetic groups”, Proc. Symp. Pure Math., IX, Amer. Math. Soc., 1966, 104–109 | MR

[10] N. D. Allan, “On the commensurability class of the Siegel modular group”, Bull. Amer. Math. Soc., 74:1 (1968), 115–118 | DOI | MR | Zbl

[11] N. D. Allan, “Maximal open compact subgroup of the projective symplectic group over a locally compact discrete valutation field”, Rev. colomb. mat., 5:3 (1971), 31–58 | MR | Zbl

[12] A. Borel, “Density and maximality of arithmetic subgroups”, J. reine und angew. Math., 224 (1966), 78–89 | MR | Zbl

[13] F. Bruhat, “Sous-groupes compacts maximaux des groupes semi-simples $p$-adiques”, Seminaire Bourbaki, no. 271, 1963/1964, 271-01–271-10 | MR

[14] F. Bruhat, “$p$-adic groups”, Proc. Symp. Pure Math., IX, Amer. Math. Soc., 1966, 63–70 | MR

[15] F. Bruhat, J. Tits, “Groupes reductifs sur un corps local”, Publ. Math. IHES, 1972, no. 41, 5–251 | MR | Zbl

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

[17] A. A. Bondarenko, “K klassifikatsii maksimalnykh arifmeticheskikh podgrupp v ortogonalnykh gruppakh tipa $(D_l)$”, DAN BSSR, 18:9 (1974), 773–776 | MR | Zbl

[18] A. A. Bondarenko, “Klassifikatsiya maksimalnykh arifmeticheskikh podgrupp v ortogonalnykh gruppakh tipa $(D_l)$”, DAN BSSR, 19:11 (1975), 969–972 | MR | Zbl