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Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble

Théorème de boone-higman, travaux de B. H. Neumann et macintyre
  • Gabriel Sabbagh
16, 17, 18 Novembre 1974
Part of the Lecture Notes in Mathematics book series (LNM, volume 514)

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Bibliographie

  1. [1]
    J.-P. AZA—Relations diophantiennes et la solution négative du dixième problème d’Hilbert. Séminaire Bourbaki, exposé 383 (Novembre 1970), Lecture Notes in Math. no 244, Springer-Verlag, 1971.Google Scholar
  2. [2]
    J. BARWISE et A. ROBINSON—Completing theories by forcing, Ann. Math. Logic, Vol. 2 (1970), 119–142.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    W. W. BOONE—Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups, Annals of Math., Vol. 84 (1966), 49–84.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    W. W. BOONE—Decision problems about algebraic and logical systems as a whole and recursively enumerble degrees of unsolvability, in Contributions to Mathematical Logic (Hannover 1966), 13–36, North-Holland, Amsterdam, 1968.Google Scholar
  5. [5]
    W. W. BOONE et G. HIGMAN—An algebraic characterization of groups with soluble word problem, Journal Austral Math. Soc., à paraître.Google Scholar
  6. [6]
    W. W. BOONE et H ROGERS Jr.—On a problem of J. H. C. Whitehead and a problem of Alonzo Church, Math. Scand., Vol. 19 (1966), 185–192.zbMATHMathSciNetGoogle Scholar
  7. [7]
    N. BOURBAKI—Algèbre I, chapitres 1 à 3, Hermann, Paris, 1970.Google Scholar
  8. [8]
    J. L. BRITTON—The world problem, Annals of Maths., Vol. 77 (1963), 16–32.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    C. C. CHANG et H. J. KEISLER—Model theory, North-Holland, Amsterdam, 1973.zbMATHGoogle Scholar
  10. [10]
    C. R. J. CLAPHAM—An embedding theorem for finitely generated groups, Proc. London Math. Soc., Vol. 17 (1967), 419–430.zbMATHMathSciNetGoogle Scholar
  11. [11]
    G. HIGMAN—Subgroups of finitely presented groups Proc. of the Royal Society, A, Vol. 262 (1961), 455–475.zbMATHMathSciNetGoogle Scholar
  12. [12]
    G. HIGMAN, B. H. NEJMANN et H. NEUMANN—Embedding theorems for groups, J. London Math. Soc., Vol. 24 (1949), 247–254.MathSciNetGoogle Scholar
  13. [13]
    H. J. KEISLER—The omitting types theorem, à paraître dans un recueil édité par Morley (Carus).Google Scholar
  14. [14]
    A. V. KUZNECOV—dans Akad. Nauk S.S.S.R. (1956), 145–146.Google Scholar
  15. [15]
    D. LACOMBE—Théorèmes de non-décidabilité, Séminaire Bourbaki, exposé 266 (février 1964), W. A. Benjamin, New York, 1966.Google Scholar
  16. [16]
    R. C. LYNDON—Metamathematics and Algebra: An example in Proc. Int. Congress Phil. Sci., Stanford, 1960.Google Scholar
  17. [17]
    A. MACINTYRE—On algebraically closed groups, Annals of Maths., Vol. 96 (1972), 53–97.zbMATHMathSciNetCrossRefGoogle Scholar
  18. [18]
    A. MACINTYRE—Omitting quantifier-free types in generic structures, Journ. of Symbolic Logic, Vol. 37 (1972), 512–520.zbMATHMathSciNetCrossRefGoogle Scholar
  19. [19]
    A. MALCEV—The metamathematics of algebraic systems, North-Holland, Amsterdam, 1971.zbMATHGoogle Scholar
  20. [20]
    R. MCKENZIE et R. J. THOMPSON—Unsolvable word problems, in Word problems: decision problems and the Burnside problem in group in group theory, North-Holland, Amsterdam, 1973, 457–478.Google Scholar
  21. [21]
    B. H. NNEUMANN—A note on algebraically closed groups, J. London Math. Soc., Vol. 27 (1952), 247–249.MathSciNetGoogle Scholar
  22. [22]
    B. H. NEUMANN—The isomorphism problem for algebraically closed groups, in Word problems: decision problems and the Burnside problem in group theory, North-Holland, Amsterdam, 1973, 553–562.Google Scholar
  23. [23]
    B. H. NEUMANN et S. YAMAMURO—Boolean powers of simple groups, Journ. Austral. Math. Soc., Vol. 5 (1965), 315–324.zbMATHMathSciNetCrossRefGoogle Scholar
  24. [24]
    M. O. RABIN—Recursive unsolvability of group theoretic problems, Annals of Maths., Vol. 67 (1958), 172–194.zbMATHMathSciNetCrossRefGoogle Scholar
  25. [25]
    M. O. RABIN—Computable algebra, general theory und theory of computable fields, Trans. Amer. Math. Soc., Vol. 95 (1960), 341–360.zbMATHMathSciNetCrossRefGoogle Scholar
  26. [26]
    M. O. RABIN—Non-standard models and independence of the induction axiom, in Essays on the foundations of Mathematics, Jerusalem, 1961, 287–299.Google Scholar
  27. [27]
    D. J. S. ROBINSON—Finiteness conditions and generalized soluble groups, Part I, Springer, Berlin, 1972.zbMATHGoogle Scholar
  28. [28]
    J. J. ROTMAN—The theory of groups: an introduction, second edition, Allyn and Bacon, Boston, 1973.Google Scholar
  29. [29]
    W. R. SCOTT—Algebraically closed groups, Proc. Amer. Math. Soc., Vol. 2 (1951), 118–121.zbMATHMathSciNetCrossRefGoogle Scholar
  30. [30]
    W. R. SCOTT—Group theory, Prentice-Hall, 1964Google Scholar
  31. [31]
    J.-P. SERRE—Groupes discrets, Collège de France, 1968/1969.Google Scholar
  32. [32]
    H. SIMMONS—The world problem for absolute presentations, J. London Math. Soc., Vol. 6 (1973), 275–280. [explicite le fait que les présentations “absolues” récursives de [22] ont un problème de mots résoluble; notre exposé a utilisé implicitement la réciproque qui est triviale.]zbMATHMathSciNetGoogle Scholar

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© N. Bourbaki 1976

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  • Gabriel Sabbagh

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