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Group extensions ofp-adic and adelic linear groups

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References

  1. American Mathematical Society,Notes on the Boulder Conference on Algebraic Groups and Discontinuous Subgroups, Summer 1965.

  2. E. Artin,Algebraic Number Theory (Notes byG. Wurges), Göttingen.

  3. -- andJ. Tate,Class Field Theory (Harvard), 1961.

  4. —— andG. Whaples, Axiomatic characterization of fields by the product formula,Bull. Amer. Math. Soc., vol. 51 (1945), pp. 469–492.

    MATH  MathSciNet  Google Scholar 

  5. —— andG. Whaples, A note on the axiomatic characterization of fields,Bull. Amer. Math. Soc., vol. 52 (1946), pp. 245–247.

    MATH  MathSciNet  Google Scholar 

  6. L. Auslander andC. Moore, Unitary representations of solvable Lie groups,American Math. Soc., Memoir no 62 (1966).

  7. S. Banach, Théorie des opérations linéaires,Monogr. Mat., t. I, Warsaw, 1932.

  8. H. Bass, M. Lazard andJ.-P. Serre, Sous-groupes d’indice fini dans SL (n,Z),Bull. Amer. Math. Soc., vol. 70 (1964), pp. 385–392.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Bass andJ. Milnor,On the congruence subgroup problem for SL n (n ≥ 3)and Sp n (n ≥2) (Notes, Institute for Advanced Study).

  10. H. Bass, J. Milnor andJ.-P. Serre,Solution of the congruence subgroup problem for SL n (n≥3)and Sp n (n ≥2),Inst. des Hautes Études Scient., no 33 (1967).

  11. A. Borel, Some finiteness properties of adèle groups over number fields,Inst. des Hautes Études Scient., no 16 (1963).

  12. -- andJ. Tits, Groupes réductifs,Inst. des Hautes Études Scient., no 27 (1965).

  13. Bourbaki,Topologie générale, chap. IX, 2e éd., Paris, Hermann, 1958.

    MATH  Google Scholar 

  14. F. Bruhat, Sur une classe de sous-groupes compacts maximaux des groupesp-adiques,Inst. des Hautes Études Scient., no 23 (1964).

  15. C. Chevalley, Sur certains groupes simples,Tôhoku Journal of Math. (2), vol. 7 (1955), pp. 14–62.

    MATH  MathSciNet  Google Scholar 

  16. --, Sur certains schémas de groupes semi-simples,Séminaire Bourbaki, Exposé 219.

  17. S. Eilenberg andS. Mac Lane, Cohomology theory in abstract groups, I,Ann. of Math. (2), vol. 48 (1947), pp. 51–78.

    Article  MathSciNet  Google Scholar 

  18. ——, Cohomology theory in abstract groups, II,Ann. of Math. (2), vol. 48 (1947), pp. 326–341.

    Article  MathSciNet  Google Scholar 

  19. R. Godement, Groupes linéaires algébriques sur un corps parfait,Séminaire Bourbaki, Exposé 206.

  20. S. Helgason,Differential Geometry and Symmetric Spaces, New York, Academic Press, 1962.

    MATH  Google Scholar 

  21. G. Hochschild andJ.-P. Serre, Cohomology of group extensions,Trans. Amer. Math. Soc., vol. 74 (1953), pp. 110–134.

    Article  MATH  MathSciNet  Google Scholar 

  22. N. Iwahori andH. Matsumoto, On some Bruhat decomposition and the structure of the Hecke ring ofp-adic Chevalley groups,Inst. des Hautes Études Scient., no 25 (1965).

  23. T. Kubota, Topological covering of SL(2) over a local field,Jour. Math. Soc. Japan, vol. 19 (1967), pp. 114–121.

    Article  MATH  MathSciNet  Google Scholar 

  24. M. Lazard, Groupes analytiquesp-adiques,Inst. des Hautes Études Scient., no 26 (1965).

  25. G. W. Mackey, Les ensembles boréliens et les extensions des groupes,J. Math. Pures et Appl., vol. 36 (1957), pp. 171–178.

    MATH  MathSciNet  Google Scholar 

  26. ——, Borel structures in groups and their duals,Trans. Amer. Math. Soc., vol. 85 (1957), pp. 134–165.

    Article  MATH  MathSciNet  Google Scholar 

  27. J. Mennicke, Finite factor groups of the unimodular group,Ann. of Math (2), vol. 81 (1965), pp. 31–37.

    Article  MathSciNet  Google Scholar 

  28. ——, Zur Theorie der Siegelische Modulgruppe,Math. Ann., vol. 159 (1965), pp. 115–129.

    Article  MATH  MathSciNet  Google Scholar 

  29. D. Montgomery andL. Zippin,Topological transformation groups, Interscience, New York, 1955.

    MATH  Google Scholar 

  30. C. C. Moore, Extensions and low dimensional cohomology theory of locally compact groups, I,Trans. Amer. Math. Soc., vol. 113 (1964), pp. 40–63.

    Article  MathSciNet  Google Scholar 

  31. ——, Extensions and low dimensional cohomology theory of locally compact groups, II,Trans. Amer. Math. Soc., vol. 113 (1964), pp. 63–86.

    Google Scholar 

  32. ——, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups,Ann. of Math (2), vol. 82 (1965), pp. 146–182.

    Article  MathSciNet  Google Scholar 

  33. J.-P. Serre,Corps locaux, Paris, Hermann, 1962.

    MATH  Google Scholar 

  34. ——,Cohomologie galoisienne, Berlin, Springer, 1964.

    MATH  Google Scholar 

  35. I. Schur, über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen,J. Reine Angew. Math., vol. 127 (1904), pp. 20–50.

    MATH  Google Scholar 

  36. Séminaire «Sophus Lie», Paris, 1954.

  37. A. Shapiro, Group extensions of compact Lie groups,Ann. of Math. (2), vol. 50 (1949), pp. 581–585.

    Article  MathSciNet  Google Scholar 

  38. Steenrod,Topology of Fiber Bundles, Princeton Univ. Press, Princeton, 1951.

    Google Scholar 

  39. R. Steinberg, Variations on a theme of Chevalley,Pacific J. of Math., vol. 9 (1959), pp. 875–891.

    MATH  MathSciNet  Google Scholar 

  40. --,Générateurs, relations et revêtements de groupes algébriques, Colloque de Bruxelles (1962), pp. 113–127.

  41. A. Weil, Sur certains groupes d’opérateurs unitaires,Acta Math., vol. 111 (1964), pp. 143–211.

    Article  MATH  MathSciNet  Google Scholar 

  42. H. Matsumoto,Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Thèse, Univ. de Paris, 1968.

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Authors
  1. Calvin C. Moore
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Research supported in part by the National Science Foundation under grant no. GP-5585.

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Moore, C.C. Group extensions ofp-adic and adelic linear groups. Publications Mathématiques de L’Institut des Hautes Scientifiques 35, 5–70 (1968). https://doi.org/10.1007/BF02698923

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