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Solution of the congruence subgroup problem for SL n (n ≥ 3) and Sp2n (n ≥ 2)

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References

  1. Bass (H.), K-theory and stable algebra,Publ. I.H.E.S., no 22 (1964), 5–60.

  2. --,Symplectic modules and groups (in preparation).

  3. Bass (H.), Heller (A.) andSwan (R.), The Whitehead group of a polynomial extension,Publ. I.H.E.S., no 22 (1964), 61–79.

  4. Bass (H.), Lazard (M.) andSerre (J.-P.), Sous-groupes d’indice fini dans SL(n,Z),Bull. Am. Math. Soc., 385–392.

  5. Bass (H.) andMilnor (J.),Unimodular groups over number fields (mimeo. notes), Princeton University (1965).

  6. --,On the congruence subgroup problem for SL n (n≥3) and Sp2n (n≥2). (Notes, Inst. for Adv. Study.)

  7. Bass (H.) andMurthy (M. P.), Grothendieck groups and Picard groups of abelian group rings,Ann. of Math., 86 (1967), 16–73.

    Article  MathSciNet  Google Scholar 

  8. Borel (A.) andHarish-Chandra, Arithmetic subgroups of algebraic groups,Ann. of Math., 75 (1962), 485–535.

    Article  MathSciNet  Google Scholar 

  9. Borel (A.) andTits (J.), Groupes réductifs,Publ. I.H.E.S., no 27 (1965), 55–151.

  10. Chevalley (C.), Sur certains schémas de groupes semi-simples,Sém. Bourbaki (1961), exposé 219.

  11. Higman (G.), On the units of group rings,Proc. Lond. Math. Soc., 46 (1940), 231–248.

    Article  MATH  MathSciNet  Google Scholar 

  12. Hurwitz (A.), Die unimodularen Substitutionen in einem algebraischen Zahlkörpen (1895),Mathematische Werke, vol. 2, 244–268, Basel (1933).

    Google Scholar 

  13. Kneser (M.), Strong approximation, I, II, Algebraic groups and discontinuous subgroups,Proc. Symp. Pure Math., IX, A.M.S., 1966, p. 187–196.

  14. Kubota (T.), Ein arithmetischer Satz über eine Matrizengrouppe,J. reine angew. Math., 222 (1965), 55–57.

    MathSciNet  Google Scholar 

  15. Matsumoto (H.), Subgroups of finite index of arithmetic groups. Algebraic groups and Discontinuous Subgroups,Proc. Symp. Pure Math., IX, A.M.S., 1966, p. 99–103.

  16. Mennicke (J.), Finite factor groups of the unimodular group,Ann. of Math., 81 (1965), 31–37.

    Article  MathSciNet  Google Scholar 

  17. ——, Zur theorie der Siegelsche Modulgruppe,Math. Ann., 159 (1965), 115–129.

    Article  MATH  MathSciNet  Google Scholar 

  18. Milnor (J.), Whitehead torsion,Bull. Am. Math. Soc., 7 (1966), 358–426.

    Article  MathSciNet  Google Scholar 

  19. Moore (C.), Extensions and low dimensional cohomology of locally compact groups, I,Trans. Am. Math. Soc., 113 (1964), 40–63.

    Article  Google Scholar 

  20. O’Meara (O. T.), On the finite generation of linear groups over Hasse domains,J. reine angew. Math., 217 (1963).

  21. Raghunathan (M. S.), A vanishing theorem for the cohomology of arithmetic subgroups of algebraic groups (to appear).

  22. Rege (N.), Finite generation of classical groups over Hasse domains (to appear).

  23. Lazard (M.), Groupes analytiquesp-adiques,Publ. I.H.E.S., no 26 (1965), 5–219.

  24. Weil (A.), Remarks on the cohomology of groups,Ann. of Math., 80 (1964), 149–157.

    Article  MathSciNet  Google Scholar 

  25. ——, Sur certains groupes d’opérateurs unitaires,Acta Math., 111 (1964), 143–211.

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. H. Bass
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  2. J. Milnor
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  3. J. -P. Serre
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Additional information

Research partially supported by the National Science Foundation under Grant N.S.F., GP-5303.

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Bass, H., Milnor, J. & Serre, J.P. Solution of the congruence subgroup problem for SL n (n ≥ 3) and Sp2n (n ≥ 2). Publications Mathématiques de l’Institut des Hautes Scientifiques 33, 59–137 (1967). https://doi.org/10.1007/BF02684586

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  • DOI: https://doi.org/10.1007/BF02684586

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