Algorithmic questions for linear algebraic groups. I
Sbornik. Mathematics, Tome 41 (1982) no. 2, pp. 149-179 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a linear algebraic group defined over the field of rational numbers and subject to certain conditions, let $G(\mathbf R)$ be its group of real points, and let $G(\mathbf Z,m)$ be a congruence-subgroup of its group of integer points. In this paper it is proved that, using a recursive procedure, one can construct a fundamental set of $G(\mathbf Z,m)$ in $G(\mathbf R)$. This result will be applied in the second part of the article. Bibliography: 18 titles.
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R. A. Sarkisyan. Algorithmic questions for linear algebraic groups. I. Sbornik. Mathematics, Tome 41 (1982) no. 2, pp. 149-179. http://geodesic.mathdoc.fr/item/SM_1982_41_2_a0/

[1] R. A. Sarkisyan, “Kogomologii Galua i nekotorye voprosy teorii algoritmov”, Matem. sb., 111(153) (1980), 579–609 | MR | Zbl

[2] by А. Борель Lineinye algebraicheskie gruppy, izd-vo “Mir”, Moskva, 1972 | MR

[3] A. Borel, Zh. Tite, “Reduktivnye gruppy”, Matematika, 11:1 (1967), 43–111; 11:2, 3–31

[4] Yu.,I. Merzlyakov, Ratsionalnye gruppy, izd-vo “Nauka”, Moskva, 1980 | MR

[5] Zh. P. Serr, Kogomologii Galua, izd-vo “Mir”, Moskva, 1968 | MR

[6] A. Borel, “Arifmeticheskie svoistva algebraicheskikh grupp”, Matematika, 8:2 (1964), 3–17 | MR

[7] M. Kneser, “Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen”, Archiv Math., 7:5 (1956), 323–332 | DOI | MR | Zbl

[8] V. P. Platonov, “O probleme roda v arifmeticheskikh gruppakh”, DAN SSSR, 200:4 (1971), 793–796 | MR | Zbl

[9] V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Chisla i gruppy klassov algebraicheskikh grupp”, Izv. AN SSSR, seriya matem., 43 (1979), 603–627 | MR | Zbl

[10] S. N. Chernikov, A. I. Zaitsev, “Shestoi Vsesoyuznyi simpozium po teorii grupp”, Uspekhi matem. nauk, 34:4(208) (1979), 239–243

[11] A. Borel, Kharish-Chandra, “Fundamentalnye mnozhestva arifmeticheskikh grupp”, Matematika, 8:2 (1964), 19–71 | MR

[12] A. Borel, “Fundamentalnye mnozhestva arifmeticheskikh grupp i avtomorfnye formy”, Matematika, 12:4 (1968), 80–103; 12:5, 34–90

[13] Dzh. Kassels i A. Frëlikh (pod red.), “Algebraicheskaya teoriya chisel”, sb. statei, izd-vo “Mir”, Moskva, 1969

[14] A. Veil, Osnovy teorii chisel, izd-vo “Mir”, Moskva, 1972 | MR

[15] G. Keisler, Ch. Ch. Chen, Teoriya modelei, izd-vo “Mir”, Moskva, 1977 | MR

[16] P. Delin, “Raboty Shimury”, Matematika, 18:1 (1974), 62–89

[17] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, izd-vo “Nauka”, Moskva, 1972 | MR

[18] R. A. Sarkisyan, “Ob odnoi probleme vkhozhdeniya dlya grupp adelei”, Matem. zametki, 25:1 (1979), 37–50 | MR | Zbl