On the congruence subgroup problem

Madabusi S. Raghunathan

Publications Mathématiques de l'IHÉS (1976)

  • Volume: 46, page 107-161
  • ISSN: 0073-8301

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Raghunathan, Madabusi S.. "On the congruence subgroup problem." Publications Mathématiques de l'IHÉS 46 (1976): 107-161. <http://eudml.org/doc/103942>.

@article{Raghunathan1976,
author = {Raghunathan, Madabusi S.},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {107-161},
publisher = {Institut des Hautes Études Scientifiques},
title = {On the congruence subgroup problem},
url = {http://eudml.org/doc/103942},
volume = {46},
year = {1976},
}

TY - JOUR
AU - Raghunathan, Madabusi S.
TI - On the congruence subgroup problem
JO - Publications Mathématiques de l'IHÉS
PY - 1976
PB - Institut des Hautes Études Scientifiques
VL - 46
SP - 107
EP - 161
LA - eng
UR - http://eudml.org/doc/103942
ER -

References

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  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. Zbl0232.20086MR28 #5117
  2. 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. Zbl0174.05203MR39 #5574
  3. BEHR (H.), 1. Endliche Erzeugbarkeit arithmetischer Gruppen über Functionenkörpern, Inv. Math., 7 (1969), 1-32. Zbl0169.34802MR39 #213
  4. BERNSTEIN (I. N.), KAZDAN (D. A.), 1. The one dimensional cohomology of discrete groups, Functional Anal. Appl., 4 (1970), 1-4. MR44 #1768
  5. BOREL (A.), 1. Introduction aux groupes arithmétiques, Paris, Hermann, 1969. Zbl0186.33202MR39 #5577
  6. BOREL (A.)2. Density properties of certain subgroups of semisimple groups, Ann. of Math., 72 (1960), 179-188. Zbl0094.24901MR23 #A964
  7. BOREL (A.), TITS (J.), 1. Groupes réductifs, Publ. Math. I.H.E.S., 27 (1965), 55-151. Zbl0145.17402MR34 #7527
  8. BOREL (A.), TITS (J.)2. Homomorphismes "abstraits" de groupes algébriques simples, Ann. of Math., 97 (1973), 499-571. Zbl0272.14013MR47 #5134
  9. CHEVALLEY (C.), 1. Deux théorèmes d'arithmétique, J. of Math. Soc. Japan, 3 (1951), 36-44. Zbl0044.03001MR13,440a
  10. CHEVALLEY (C.)2. Sur certains schémas de groupes semi-simples, Sém. Bourbaki, Exposé 219, New York, Benjamin, 1966. 
  11. CHEVALLEY (C.)3. Sur certains groupes simples, Tohoku J. of Math. (2), 7 (1955), 14-62. Zbl0066.01503MR17,457c
  12. DELAROCHE (C.), KIRILLOV (A.), Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés (d'après D. A. Kazdan), Sém. Bourbaki 1967/1968, Exposé 343, New York, Benjamin, 1969. Zbl0214.04602
  13. DEODHAR (V. V.), 1. On central extensions of rational points of algebraic groups (to appear). Zbl0306.20041
  14. DIEUDONNÉ (J.), 1. La géométrie des groupes classiques, Berlin, Springer-Verlag, 1955. Zbl0067.26104MR17,236a
  15. DIEUDONNÉ (J.)2. On the structure of unitary groups (II), Amer. J. Math., 75 (1953), 665-678. Zbl0051.01803MR15,287f
  16. GARLAND (H.), 1. p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math., 97 (1973), 376-423. Zbl0262.22010MR47 #8719
  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. Zbl0206.03603MR42 #1943
  18. HARDER (G.), 1. Minkowskische Reductionstheorie über Functionenkörpern, Inv. Math., 7 (1969), 33-54. Zbl0242.20046MR44 #1667
  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. Zbl0168.27602MR35 #288
  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. Zbl0186.37003
  21. LANG (S.), 1. Algebraic groups over finite fields, Amer. J. of Math., 78 (1956), 555-563. Zbl0073.37901MR19,174a
  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. Zbl0336.57037
  23. MATSUMOTO (M.), 1. Sur les sous-groupes arithmétiques des groupes semisimples déployés, Ann. E.N.S. (4), 2 (1969), 1-62. Zbl0261.20025
  24. MENNICKE (J.), 1. Finite factor groups of the unimodular group, Ann. of Math., 81 (1965), 31-37. Zbl0135.06504MR30 #2083
  25. MENNICKE (J.)2. Zur theorie der Siegelsche Modulgruppe, Math. Ann., 159 (1965), 115-129. Zbl0134.26502MR31 #5903
  26. MOORE (C. C.), 1. Group extensions of p-adic and adelic linear groups, Publ. Math. I.H.E.S., 35 (1969), 5-70. Zbl0159.03203
  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. Zbl0217.36301
  28. PLATONOV (V. P.)2. Maximal arithmetic groups (to appear). Zbl1214.20045
  29. PLATONOV (V. P.)3. To appear. 
  30. RAGHUNATHAN (M. S.), 1. Cohomology of arithmetic subgroups of algebraic groups: 1, Ann. of Math., 86 (1967), 409-424. Zbl0157.06802MR37 #2898
  31. RAGHUNATHAN (M. S.)2. Cohomology of arithmetic subgroups of algebraic groups: II, Ann. of Math., 87 (1968), 279-304. Zbl0157.06803MR37 #2898
  32. RAGHUNATHAN (M. S.)3. Discrete Subgroups of Lie groups, Berlin, Springer-Verlag, 1972. Zbl0254.22005MR58 #22394a
  33. RAGHUNATHAN (M. S.)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. Zbl0239.20063MR42 #7671
  35. SERRE (J.-P.)2. Cohomologie des groupes discrets, in Prospects in Mathematics, Princeton, 1970. 
  36. STEINBERG (R.), 1. Variations on a theme of Chevalley, Pacific J. of Math., 9 (1959), 875-891. Zbl0092.02505MR22 #79
  37. STEINBERG (R.)2. Générateurs, relations et revêtements de groupes algébriques, Colloque de Bruxelles (1962), 113-127. Zbl0272.20036MR27 #3638
  38. STEINBERG (R.)3. Lectures on Chevalley groups, Yale University, 1968. MR57 #6215
  39. TITS (J.), 1. Algebraic and abstract simple groups, Ann. of Math., 80 (1964), 313-329. Zbl0131.26501MR29 #2259
  40. TITS (J.)2. Classification of algebraic semisimple groups, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., 1966. Zbl0238.20052MR37 #309
  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). Zbl0087.02202
  43. WANG (S. P.), 1. The dual space of semisimple Lie groups, Amer. J. Math., 91 (1969), 921-937. Zbl0192.36102
  44. WEIL (A.), 1. Discrete subgroups of Lie groups, II, Ann. of Math., 75 (1962), 578-602. Zbl0131.26602MR25 #1242
  45. WEIL (A.)2. Adèles and algebraic groups, Institute for Adv. Study, Princeton, 1961. 
  46. WEIL (A.)3. Remarks on the cohomology of groups, Ann. of Math., 80 (1964), 149-157. Zbl0192.12802MR30 #199

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