Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble (théorème de Boone-Higman, travaux de B. H. Neumann et MacIntyre)
Séminaire Bourbaki : vol. 1974/75, exposés 453-470, Séminaire Bourbaki, no. 17 (1976), Exposé no. 457, 20 p.
@incollection{SB_1974-1975__17__61_0,
     author = {Sabbagh, Gabriel},
     title = {Caract\'erisation alg\'ebrique des groupes de type fini ayant un probl\`eme de mots r\'esoluble (th\'eor\`eme de {Boone-Higman,} travaux de {B.} {H.} {Neumann} et {MacIntyre)}},
     booktitle = {S\'eminaire Bourbaki : vol. 1974/75, expos\'es 453-470},
     series = {S\'eminaire Bourbaki},
     note = {talk:457},
     pages = {61--80},
     publisher = {Springer-Verlag},
     number = {17},
     year = {1976},
     mrnumber = {446941},
     zbl = {0366.20023},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1974-1975__17__61_0/}
}
TY  - CHAP
AU  - Sabbagh, Gabriel
TI  - Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble (théorème de Boone-Higman, travaux de B. H. Neumann et MacIntyre)
BT  - Séminaire Bourbaki : vol. 1974/75, exposés 453-470
AU  - Collectif
T3  - Séminaire Bourbaki
N1  - talk:457
PY  - 1976
SP  - 61
EP  - 80
IS  - 17
PB  - Springer-Verlag
UR  - http://www.numdam.org/item/SB_1974-1975__17__61_0/
LA  - fr
ID  - SB_1974-1975__17__61_0
ER  - 
%0 Book Section
%A Sabbagh, Gabriel
%T Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble (théorème de Boone-Higman, travaux de B. H. Neumann et MacIntyre)
%B Séminaire Bourbaki : vol. 1974/75, exposés 453-470
%A Collectif
%S Séminaire Bourbaki
%Z talk:457
%D 1976
%P 61-80
%N 17
%I Springer-Verlag
%U http://www.numdam.org/item/SB_1974-1975__17__61_0/
%G fr
%F SB_1974-1975__17__61_0
Sabbagh, Gabriel. Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble (théorème de Boone-Higman, travaux de B. H. Neumann et MacIntyre), dans Séminaire Bourbaki : vol. 1974/75, exposés 453-470, Séminaire Bourbaki, no. 17 (1976), Exposé no. 457, 20 p. http://www.numdam.org/item/SB_1974-1975__17__61_0/

[1] J.-P. Azra - Relations diophantiennes et la solution négative du dixième problème d'Hilbert, Séminaire Bourbaki, exposé 383 (Novembre 1970), Lecture Notes in Math. n° 244, Springer-Verlag, 1971. | Numdam | MR | Zbl

[2] J. Barwise et A. Robinson - Completing theories by forcing, Ann. Math. Logic, Vol. 2 (1970), 119-142. | MR | Zbl

[3] W.W. Boone - Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups, Annals of Maths., Vol. 84 (1966), 49-84. | MR | Zbl

[4] W.W. Boone - Decision problems about algebraic and logical systems as a whole and recursively enumerable degrees of unsolvability, in Contributions to Mathematical Logic (Hannover 1966), 13-36, North-Holland, Amsterdam, 1968. | MR | Zbl

[5] W.W. Boone et G. Higman - An algebraic characterization of groups with soluble word problem, Journal Austral Math. Soc., à paraître. | Zbl

[6] W.W. Boone et H. Rogers Jr. - On a problem of J. H. C. Whitehead and a problem cf Alonzo Church, Math. Scand., Vol. 19 (1966), 185-192. | MR | Zbl

[7] N. Bourbaki - Algèbre I, chapitres 1 à 3, Hermann, Paris, 1970. | MR | Zbl

[8] J.L. Britton - The word problem, Annals of Maths., Vol. 77 (1963), 16-32. | MR | Zbl

[9] C.C. Chang et H.J. Keisler - Model theory, North-Holland, Amsterdam, 1973. | Zbl

[10] C.R.J. Clapham - An embedding theorem for finitely generated groups, Proc. London Math. Soc., Vol. 17 (1967), 419-430. | MR | Zbl

[11] G. Higman - Subgroups of finitely presented groups, Proc. of the Royal Society, A, Vol. 262 (1961), 455-475. | MR | Zbl

[12] G. Higman, B.H. Neumann et H. Neumann - Embedding theorems for groups, J. London Math. Soc., Vol. 24 (1949), 247-254. | MR | Zbl

[13] H.J. Keisler - The omitting types theorem, à paraître dans un recueil édité par Morley (Carus).

[14] A.V. Kuznecov - dans Akad. Nauk S.S.S.R. (1956), 145-146.

[15] D. Lacombe - Théorèmes de non-décidabilité, Séminaire Bourbaki, exposé 266 (février 1964), W. A. Benjamin, New York, 1966. | Numdam | MR | Zbl

[16] R.C. Lyndon - Metamathematics and Algebra : An example in Proc. Int. Congress Phil. Sci., Stanford, 1960. | Zbl

[17] A. Macintyre - On algebraically closed groups, Annals of Maths., Vol. 96 (1972), 53-97. | MR | Zbl

[18] A. Macintyre - Omitting quantifier-free types in generic structures, Journ. of Symbolic Logic, Vol. 37 (1972), 512-520. | MR | Zbl

[19] A. Malcev - The metamathematics of algebraic systems, North-Holland, Amsterdam, 1971. | MR

[20] R. Mckenzie et R.J. Thompson - Unsolvable word problems, in Word problems : decision problems and the Burnside problem in group theory, North-Holland, Amsterdam, 1973, 457-478. | MR | Zbl

[21] B.H. Neumann - A note on algebraically closed groups, J. London Math. Soc., Vol. 27 (1952), 247-249. | MR | Zbl

[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. | MR | Zbl

[23] B.H. Neumann et S. Yamamuro - Boolean powers of simple groups, Journ. Austral. Math. Soc., Vol. 5 (1965), 315-324. | MR | Zbl

[24] M.O. Rabin - Recursive unsolvability of group theoretic problems, Annals of Maths., Vol. 67 (1958), 172-194. | MR | Zbl

[25] M.O. Rabin - Computable algebra, general theory and theory of computable fields, Trans. Amer. Math. Soc., Vol. 95 (1960), 341-360. | MR | Zbl

[26] M.O. Rabin - Non-standard models and independence of the induction axiom, in Essays on the foundations of Mathematics, Jerusalem, 1961, 287-299. | MR | Zbl

[27] D.J.S. Robinson - Finiteness conditions and generalized soluble groups, Part I, Springer, Berlin, 1972. | Zbl

[28] J.J. Rotman - The theory of groups : an introduction, second edition, Allyn and Bacon, Boston, 1973. | MR | Zbl

[29] W.R. Scott - Algebraically closed groups, Proc. Amer. Math. Soc., Vol. 2 (1951), 118-121. | MR | Zbl

[30] W.R. Scott - Group theory, Prentice-Hall, 1964. | MR | Zbl

[31] J.-P. Serre - Groupes discrets, Collège de France, 1968/1969.

[32] H. Simmons - The word 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.] | MR | Zbl