×

zbMATH — the first resource for mathematics

On the congruence subgroup problem. (English) Zbl 0347.20027

MSC:
20G30 Linear algebraic groups over global fields and their integers
11R99 Algebraic number theory: global fields
14L99 Algebraic groups
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] Bass (H.), Lazard (M.), Serre (J.-P.), 1. Sous-groupes d’indices finis dans SL(n, Z),Bull. Amer. Math. Soc.,70 (1964), 385–392. · Zbl 0232.20086 · doi:10.1090/S0002-9904-1964-11107-1
[2] Bass (H.), Milnor (J.), Serre (J.-P.), 1. Solutions of the congruence subgroup problem for SL(n) (n) and Sp(2n) (n),Publ. Math. I.H.E.S.,33 (1967), 59–137. · Zbl 0174.05203
[3] Behr (H.), 1. Endliche Erzeugbarkeit arithmetischer Gruppen über Functionenkörpern,Inv. Math.,7 (1969), 1–32. · Zbl 0169.34802 · doi:10.1007/BF01418772
[4] Bernstein (I. N.), Kazdan (D. A.), 1. The one dimensional cohomology of discrete groups,Functional Anal. Appl.,4 (1970), 1–4. · Zbl 0207.03902 · doi:10.1007/BF01075614
[5] Borel (A.), 1.Introduction aux groupes arithmétiques, Paris, Hermann, 1969. · Zbl 0186.33202
[6] —-, 2. Density properties of certain subgroups of semisimple groups,Ann. of Math.,72 (1960), 179–188. · Zbl 0094.24901 · doi:10.2307/1970150
[7] Borel (A.), Tits (J.), 1. Groupes réductifs,Publ. Math. I.H.E.S.,27 (1965), 55–151.
[8] —-, —-, 2. Homomorphismes “ abstraits ” de groupes algébriques simples,Ann. of Math.,97 (1973), 499–571. · Zbl 0272.14013 · doi:10.2307/1970833
[9] Chevalley (C.), 1. Deux théorèmes d’arithmétique,J. of Math. Soc. Japan,3 (1951), 36–44. · Zbl 0044.03001 · doi:10.2969/jmsj/00310036
[10] —- 2. Sur certains schémas de groupes semi-simples,Sém. Bourbaki, Exposé 219, New York, Benjamin, 1966.
[11] —- 3. Sur certains groupes simples,Tohoku J. of Math. (2),7 (1955), 14–62. · Zbl 0066.01503 · doi:10.2748/tmj/1178245104
[12] Delaroche (C.), Kirillov (A.), Sur les relations entre l’espace dual d’un groupe et la structure de ses sousgroupes fermés (d’après D. A. Kazdan),Sém. Bourbaki 1967/68, Exposé 343, New York, Benjamin, 1969.
[13] Deodhar (V. V.), 1.On central extensions of rational points of algebraic groups (to appear). · Zbl 0392.20027
[14] Dieudonné (J.), 1.La géométrie des groupes classiques, Berlin, Springer-Verlag, 1955.
[15] —- 2. On the structure of unitary groups (II),Amer. J. Math.,75 (1953), 665–678. · Zbl 0051.01803 · doi:10.2307/2372541
[16] Garland (H.), 1.p-adic curvature and the cohomology of discrete subgroups ofp-adic groups,Ann. of Math.,97 (1973), 376–423. · Zbl 0262.22010 · doi:10.2307/1970829
[17] Garland (H.), Raghunathan (M. S.), 1. Fundamental domains for lattices in (R-) rank one semisimple Lie groups,Ann. of Math.,92 (1970), 279–326. · Zbl 0206.03603 · doi:10.2307/1970838
[18] Harder (G.), 1. Minkowskische Reductionstheorie über Functionenkörpern,Inv. Math.,7 (1969), 33–54. · Zbl 0242.20046 · doi:10.1007/BF01418773
[19] Kazdan (D. A.), Connection on the dual space of a group with the structure of its closed subgroups,Functional Anal. Appl.,1 (1967), 63–65. · Zbl 0168.27602 · doi:10.1007/BF01075866
[20] Kneser (M.), 1. Normal subgroups of integral orthogonal groups in algebraic K-theory and its geometric applications,Lecture Notes in Maths. 108, Berlin, Springer-Verlag.
[21] Lang (S.), 1. Algebraic groups over finite fields,Amer. J. of Math.,78 (1956), 555–563. · Zbl 0073.37901 · doi:10.2307/2372673
[22] Margulis (G. A.), 1. Discrete Groups of Motions of manifolds of non-positive curvature (en russe),Proc. Intern. Congress of Math., Vancouver 1974, vol. 2, 21–34.
[23] Matsumoto (M.), 1. Sur les sous-groupes arithmétiques des groupes semisimples déployés,Ann. E.N.S. (4),2 (1969), 1–62. · Zbl 0261.20025
[24] Mennicke (J.), 1. Finite factor groups of the unimodular group,Ann. of Math.,81 (1965), 31–37. · Zbl 0135.06504 · doi:10.2307/1970380
[25] —- 2. Zur theorie der Siegelsche Modulgruppe,Math. Ann.,159 (1965), 115–129. · Zbl 0134.26502 · doi:10.1007/BF01360285
[26] Moore (C. C.), 1. Group extensions ofp-adic and adelic linear groups,Publ. Math. I.H.E.S.,35 (1969), 5–70.
[27] Platonov (V. P.), 1. The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups,Math. USSR-Izvestiya,3 (1969), 1139–1147. · Zbl 0217.36301 · doi:10.1070/IM1969v003n06ABEH000838
[28] – 2. Maximal arthmetic groups (to appear).
[29] – 3. To appear.
[30] Raghunathan (M. S.), 1. Cohomology of arithmetic subgroups of algebraic groups: 1,Ann. of Math.,86 (1967), 409–424. · Zbl 0157.06802 · doi:10.2307/1970607
[31] —- 2. Cohomology of arithmetic subgroups of algebraic groups: II,Ann. of Math.,87 (1968), 279–304. · Zbl 0157.06803 · doi:10.2307/1970585
[32] —- 3.Discrete Subgroups of Lie groups, Berlin, Springer-Verlag, 1972. · Zbl 0254.22005
[33] – 4. A note on the Kneser-Tits conjecture for global fields (to appear).
[34] Serre (J.-P.), 1. Le problème des groupes de congruence pour SL2,Ann. of Math.,92 (1970), 489–527. · Zbl 0239.20063 · doi:10.2307/1970630
[35] – 2. Cohomologie des groupes discrets, inProspects in Mathematics, Princeton, 1970.
[36] Steinberg (R.), 1. Variations on a theme of Chevalley,Pacific J. of Math.,9 (1959), 875–891. · Zbl 0092.02505
[37] – 2. Générateurs, relations et revêtements de groupes algébriques,Colloque de Bruxelles (1962), 113–127.
[38] – 3.Lectures on Chevalley groups, Yale University, 1968. · Zbl 1196.22001
[39] Tits (J.), 1. Algebraic and abstract simple groups,Ann. of Math.,80 (1964), 313–329. · Zbl 0131.26501 · doi:10.2307/1970394
[40] – 2. Classification of algebraic semisimple groups,Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., 1966. · Zbl 0238.20052
[41] Vasserstein (L. I.), 1. Subgroups of finite index in Spin groups of rank 2 (Russian),Mat. Sbornik,75 (1968), 178–184.
[42] Wall (G. E.), 1. The structure of a unitary factor group,Publ. Math. I.H.E.S.,1 (1959). · Zbl 0087.02202
[43] Wang (S. P.), 1. The dual space of semisimple Lie groups,Amer. J. Math.,91 (1969), 921–937. · Zbl 0192.36102 · doi:10.2307/2373310
[44] Weil (A.), 1. Discrete subgroups of Lie groups, II,Ann. of Math.,75 (1962), 578–602. · Zbl 0131.26602 · doi:10.2307/1970212
[45] —-, 2.Adèles and algebraic groups, Institute for Adv. Study, Princeton, 1961.
[46] —- 3. Remarks on the cohomology of groups,Ann. of Math.,80 (1964), 149–157. · Zbl 0192.12802 · doi:10.2307/1970495
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.