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Bulletin of the American Mathematical Society

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Word problems


Author: Trevor Evans
Journal: Bull. Amer. Math. Soc. 84 (1978), 789-802
MSC (1970): Primary 02F47, 02E10; Secondary 08A15, 08A25
MathSciNet review: 0498063
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  • 1. G. Bergman, The diamond lemma in ring theory, Advances in Math, (to appear).
  • 2. William W. Boone, The word problem, Ann. of Math. (2) 70 (1959), 207–265. MR 0179237
  • 3. William W. Boone and Graham Higman, An algebraic characterization of groups with soluble word problem, J. Austral. Math. Soc. 18 (1974), 41–53. Collection of articles dedicated to the memory of Hanna Neumann, IX. MR 0357625
  • 4. M. Dehn, Über unendliche diskontinuierliche Gruppen, Math. Ann. 71 (1911), 116—144.
  • 5. V. H. Dyson, The word problem and residually finite groups, Notices Amer. Math. Soc. 11 (1964), 743.
  • 6. Trevor Evans, The word problem for abstract algebras, J. London Math. Soc. 26 (1951), 64–71. MR 0038958
  • 7. Trevor Evans, Embeddability and the word problem, J. London Math. Soc. 28 (1953), 76–80. MR 0053915
  • 8. Trevor Evans, On multiplicative systems defined by generators and relations. I. Normal form theorems, Proc. Cambridge Philos. Soc. 47 (1951), 637–649. MR 0043764
  • 9. Trevor Evans, On multiplicative systems defined by generators and relations. II. Monogenic loops, Proc. Cambridge Philos Soc. 49 (1953), 579–589. MR 0057865
  • 10. Trevor Evans, Some connections between residual finiteness, finite embeddability and the word problem, J. London Math. Soc. (2) 1 (1969), 399–403. MR 0249344
  • 11. Trevor Evans, Identities and relations in commutative Moufang loops, J. Algebra 31 (1974), 508–513. MR 0348025
  • 12. Trevor Evans, Some solvable word problems, Word problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), Stud. Logic Foundations Math., vol. 95, North-Holland, Amsterdam-New York, 1980, pp. 87–100. MR 579941
  • 13. T. Evans, K. I. Mandelberg, and M. F. Neff, Embedding algebras with solvable word problems in simple algebras—some Boone-Higman type theorems, Logic Colloquium ’73 (Bristol, 1973) North-Holland, Amsterdam, 1975, pp. 259–277. Studies in Logic and the Foundations of Mathematics, Vol. 80. MR 0389568
  • 14. K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. MR 0087652
  • 15. È. A. Golubov, Finite approximability, finite separability and semigroup-theoretic constructions, First All-Union Symposium on the Theory of Semigroups (Russian), Ural. Gos. Univ., Sverdlovsk, 1969, pp. 18–23 (Russian). MR 0258989
  • 16. A. A. Gvaramija and M. M. Gluhov, A solution of the fundamental algorithmic problems in certain classes of quasigroups with identities, Sibirsk. Mat. Ž. 10 (1969), 297–317 (Russian). MR 0241561
  • 17. Marshall Hall Jr., Coset representations in free groups, Trans. Amer. Math. Soc. 67 (1949), 421–432. MR 0032642, 10.1090/S0002-9947-1949-0032642-4
  • 18. P. Hall, Some word-problems, J. London Math. Soc. 33 (1958), 482–496. MR 0102540
  • 19. G. Higman, Subgroups of finitely presented groups, Proc. Roy. Soc. Ser. A 262 (1961), 455–475. MR 0130286
  • 20. J. Kalicki, On comparison of finite algebras, Proc. Amer. Math. Soc. 3 (1952), 36–40. MR 0047584, 10.1090/S0002-9939-1952-0047584-3
  • 21. A. V. Kuznecov, O problemah tozdestva i funkcionalnoi polnoty dlja algebraiceskin system, in Trudy 3-go Vsesojuznono Mat. S"ezda, Vol. 2. (Dokl. Akad. Nauk SSSR, Moscow, 1956), 145-146.
  • 22. A. V. Kuznecov, Uspehi Mat. Nauk., 3rd issue (1958), 240.
  • 23. M. M. Lesohin, Approximability of semigroups and separability of subsemigroups, Interuniv. Sci. Sympos. General Algebra (Russian), Tartu. Gos. Univ., Tartu, 1966, pp. 52–62 (Russian). MR 0206132
  • 24. Charles C. Lindner and Trevor Evans, Finite embedding theorems for partial designs and algebras, Les Presses de l’Université de Montréal, Montreal, Que., 1977. Séminaire de Mathématiques Supérieures, No. 56 (Été 1971). MR 0460213
  • 25. A. I. Malcev, On homomorphisms onto finite groups, Učen Zap. Ivanovsk Ped. Inst. 18 (1958), 49-60.
  • 26. Anatoliĭ Ivanovič Mal′cev, The metamathematics of algebraic systems. Collected papers: 1936–1967, North-Holland Publishing Co., Amsterdam-London, 1971. Translated, edited, and provided with supplementary notes by Benjamin Franklin Wells, III; Studies in Logic and the Foundations of Mathematics, Vol. 66. MR 0349383
  • 27. Ralph McKenzie, On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model, J. Symbolic Logic 40 (1975), 186–196. MR 0376323
  • 28. Stephen Meskin, A finitely generated residually finite group with an unsolvable word problem, Proc. Amer. Math. Soc. 43 (1974), 8–10. MR 0335645, 10.1090/S0002-9939-1974-0335645-5
  • 29. K. A. Mihaĭlova, The occurrence problem for direct products of groups, Dokl. Akad. Nauk SSSR 119 (1958), 1103–1105 (Russian). MR 0100018
  • 30. V. L. Murskiĭ, Isomorphic imbeddability of a semigroup with an enumerable set of defining relations into a finitely presented semigroup, Mat. Zametki 1 (1967), 217–224 (Russian). MR 0210800
  • 31. P. S. Novikov, On the algorithmic insolvability of the word problem in group theory, American Mathematical Society Translations, Ser 2, Vol. 9, American Mathematical Society, Providence, R. I., 1958, pp. 1–122. MR 0092784
  • 32. Morris Orzech and Luis Ribes, Residual finiteness and the Hopf property in rings, J. Algebra 15 (1970), 81–88. MR 0255587
  • 33. Emil L. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic 12 (1947), 1–11. MR 0020527
  • 34. Dana Scott, Equationally complete extensions of finite algebras, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 35–38. MR 0082960
  • 35. A Thue, Probleme über Veranderungen von Zeichenreihen nach gegebenen Reglen, Skr. Vid. Kristiana I. 10 (1914).
  • 36. Philip M. Whitman, Free lattices, Ann. of Math. (2) 42 (1941), 325–330. MR 0003614

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DOI: https://doi.org/10.1090/S0002-9904-1978-14516-9