References
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.
Bass (H.), Milnor (J.), Serre (J.-P.), 1. Solutions of the congruence subgroup problem for SL(n) (n⩾3) and Sp(2n) (n⩾2),Publ. Math. I.H.E.S.,33 (1967), 59–137.
Behr (H.), 1. Endliche Erzeugbarkeit arithmetischer Gruppen über Functionenkörpern,Inv. Math.,7 (1969), 1–32.
Bernstein (I. N.), Kazdan (D. A.), 1. The one dimensional cohomology of discrete groups,Functional Anal. Appl.,4 (1970), 1–4.
Borel (A.), 1.Introduction aux groupes arithmétiques, Paris, Hermann, 1969.
——, 2. Density properties of certain subgroups of semisimple groups,Ann. of Math.,72 (1960), 179–188.
Borel (A.), Tits (J.), 1. Groupes réductifs,Publ. Math. I.H.E.S.,27 (1965), 55–151.
——, ——, 2. Homomorphismes « abstraits » de groupes algébriques simples,Ann. of Math.,97 (1973), 499–571.
Chevalley (C.), 1. Deux théorèmes d’arithmétique,J. of Math. Soc. Japan,3 (1951), 36–44.
—— 2. Sur certains schémas de groupes semi-simples,Sém. Bourbaki, Exposé 219, New York, Benjamin, 1966.
—— 3. Sur certains groupes simples,Tohoku J. of Math. (2),7 (1955), 14–62.
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.
Deodhar (V. V.), 1.On central extensions of rational points of algebraic groups (to appear).
Dieudonné (J.), 1.La géométrie des groupes classiques, Berlin, Springer-Verlag, 1955.
—— 2. On the structure of unitary groups (II),Amer. J. Math.,75 (1953), 665–678.
Garland (H.), 1.p-adic curvature and the cohomology of discrete subgroups ofp-adic groups,Ann. of Math.,97 (1973), 376–423.
Garland (H.), Raghunathan (M. S.), 1. Fundamental domains for lattices in (R-) rank one semisimple Lie groups,Ann. of Math.,92 (1970), 279–326.
Harder (G.), 1. Minkowskische Reductionstheorie über Functionenkörpern,Inv. Math.,7 (1969), 33–54.
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.
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.
Lang (S.), 1. Algebraic groups over finite fields,Amer. J. of Math.,78 (1956), 555–563.
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.
Matsumoto (M.), 1. Sur les sous-groupes arithmétiques des groupes semisimples déployés,Ann. E.N.S. (4),2 (1969), 1–62.
Mennicke (J.), 1. Finite factor groups of the unimodular group,Ann. of Math.,81 (1965), 31–37.
—— 2. Zur theorie der Siegelsche Modulgruppe,Math. Ann.,159 (1965), 115–129.
Moore (C. C.), 1. Group extensions ofp-adic and adelic linear groups,Publ. Math. I.H.E.S.,35 (1969), 5–70.
Platonov (V. P.), 1. The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups,Math. USSR-Izvestiya,3 (1969), 1139–1147.
-- 2. Maximal arthmetic groups (to appear).
-- 3. To appear.
Raghunathan (M. S.), 1. Cohomology of arithmetic subgroups of algebraic groups: 1,Ann. of Math.,86 (1967), 409–424.
—— 2. Cohomology of arithmetic subgroups of algebraic groups: II,Ann. of Math.,87 (1968), 279–304.
—— 3.Discrete Subgroups of Lie groups, Berlin, Springer-Verlag, 1972.
-- 4. A note on the Kneser-Tits conjecture for global fields (to appear).
Serre (J.-P.), 1. Le problème des groupes de congruence pour SL2,Ann. of Math.,92 (1970), 489–527.
-- 2. Cohomologie des groupes discrets, inProspects in Mathematics, Princeton, 1970.
Steinberg (R.), 1. Variations on a theme of Chevalley,Pacific J. of Math.,9 (1959), 875–891.
-- 2. Générateurs, relations et revêtements de groupes algébriques,Colloque de Bruxelles (1962), 113–127.
-- 3.Lectures on Chevalley groups, Yale University, 1968.
Tits (J.), 1. Algebraic and abstract simple groups,Ann. of Math.,80 (1964), 313–329.
-- 2. Classification of algebraic semisimple groups,Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., 1966.
Vasserstein (L. I.), 1. Subgroups of finite index in Spin groups of rank 2 (Russian),Mat. Sbornik,75 (1968), 178–184.
Wall (G. E.), 1. The structure of a unitary factor group,Publ. Math. I.H.E.S.,1 (1959).
Wang (S. P.), 1. The dual space of semisimple Lie groups,Amer. J. Math.,91 (1969), 921–937.
Weil (A.), 1. Discrete subgroups of Lie groups, II,Ann. of Math.,75 (1962), 578–602.
——, 2.Adèles and algebraic groups, Institute for Adv. Study, Princeton, 1961.
—— 3. Remarks on the cohomology of groups,Ann. of Math.,80 (1964), 149–157.
Author information
Authors and Affiliations
About this article
Cite this article
Raghunathan, M.S. On the congruence subgroup problem. Publications Mathématiques de L’Institut des Hautes Scientifiques 46, 107–161 (1976). https://doi.org/10.1007/BF02684320
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02684320