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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

16, 17, 18 Novembre 1974

Part of the Lecture Notes in Mathematics book series (LNM,volume 514)

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Bibliographie

  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. J. BARWISE et A. ROBINSON—Completing theories by forcing, Ann. Math. Logic, Vol. 2 (1970), 119–142.

    CrossRef  MATH  MathSciNet  Google Scholar 

  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.

    CrossRef  MATH  MathSciNet  Google Scholar 

  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. W. W. BOONE et G. HIGMAN—An algebraic characterization of groups with soluble word problem, Journal Austral Math. Soc., à paraître.

    Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  7. N. BOURBAKI—Algèbre I, chapitres 1 à 3, Hermann, Paris, 1970.

    Google Scholar 

  8. J. L. BRITTON—The world problem, Annals of Maths., Vol. 77 (1963), 16–32.

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. C. C. CHANG et H. J. KEISLER—Model theory, North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  10. C. R. J. CLAPHAM—An embedding theorem for finitely generated groups, Proc. London Math. Soc., Vol. 17 (1967), 419–430.

    MATH  MathSciNet  Google Scholar 

  11. G. HIGMAN—Subgroups of finitely presented groups Proc. of the Royal Society, A, Vol. 262 (1961), 455–475.

    MATH  MathSciNet  Google Scholar 

  12. G. HIGMAN, B. H. NEJMANN et H. NEUMANN—Embedding theorems for groups, J. London Math. Soc., Vol. 24 (1949), 247–254.

    MathSciNet  Google Scholar 

  13. H. J. KEISLER—The omitting types theorem, à paraître dans un recueil édité par Morley (Carus).

    Google Scholar 

  14. A. V. KUZNECOV—dans Akad. Nauk S.S.S.R. (1956), 145–146.

    Google Scholar 

  15. D. LACOMBE—Théorèmes de non-décidabilité, Séminaire Bourbaki, exposé 266 (février 1964), W. A. Benjamin, New York, 1966.

    Google Scholar 

  16. R. C. LYNDON—Metamathematics and Algebra: An example in Proc. Int. Congress Phil. Sci., Stanford, 1960.

    Google Scholar 

  17. A. MACINTYRE—On algebraically closed groups, Annals of Maths., Vol. 96 (1972), 53–97.

    CrossRef  MATH  MathSciNet  Google Scholar 

  18. A. MACINTYRE—Omitting quantifier-free types in generic structures, Journ. of Symbolic Logic, Vol. 37 (1972), 512–520.

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. A. MALCEV—The metamathematics of algebraic systems, North-Holland, Amsterdam, 1971.

    MATH  Google Scholar 

  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. B. H. NNEUMANN—A note on algebraically closed groups, J. London Math. Soc., Vol. 27 (1952), 247–249.

    MathSciNet  Google Scholar 

  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. B. H. NEUMANN et S. YAMAMURO—Boolean powers of simple groups, Journ. Austral. Math. Soc., Vol. 5 (1965), 315–324.

    CrossRef  MATH  MathSciNet  Google Scholar 

  24. M. O. RABIN—Recursive unsolvability of group theoretic problems, Annals of Maths., Vol. 67 (1958), 172–194.

    CrossRef  MATH  MathSciNet  Google Scholar 

  25. M. O. RABIN—Computable algebra, general theory und theory of computable fields, Trans. Amer. Math. Soc., Vol. 95 (1960), 341–360.

    CrossRef  MATH  MathSciNet  Google Scholar 

  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. D. J. S. ROBINSON—Finiteness conditions and generalized soluble groups, Part I, Springer, Berlin, 1972.

    MATH  Google Scholar 

  28. J. J. ROTMAN—The theory of groups: an introduction, second edition, Allyn and Bacon, Boston, 1973.

    Google Scholar 

  29. W. R. SCOTT—Algebraically closed groups, Proc. Amer. Math. Soc., Vol. 2 (1951), 118–121.

    CrossRef  MATH  MathSciNet  Google Scholar 

  30. W. R. SCOTT—Group theory, Prentice-Hall, 1964

    Google Scholar 

  31. J.-P. SERRE—Groupes discrets, Collège de France, 1968/1969.

    Google Scholar 

  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.]

    MATH  MathSciNet  Google Scholar 

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Sabbagh, G. (1976). Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble. In: Séminaire Bourbaki vol. 1974/75 Exposés 453–470. Lecture Notes in Mathematics, vol 514. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0080058

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  • DOI: https://doi.org/10.1007/BFb0080058

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