Word problems

Evans, Trevor

doi:10.1090/S0002-9904-1978-14516-9

Word problems
HTML articles powered by AMS MathViewer

by Trevor Evans PDF

Bull. Amer. Math. Soc. 84 (1978), 789-802

References

William W. Boone, The word problem, Ann. of Math. (2) 70 (1959), 207–265. MR 179237, DOI 10.2307/1970103
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, DOI 10.1017/S1446788700019108
Trevor Evans, The word problem for abstract algebras, J. London Math. Soc. 26 (1951), 64–71. MR 38958, DOI 10.1112/jlms/s1-26.1.64
Trevor Evans, Embeddability and the word problem, J. London Math. Soc. 28 (1953), 76–80. MR 53915, DOI 10.1112/jlms/s1-28.1.76
Trevor Evans, On multiplicative systems defined by generators and relations. I. Normal form theorems, Proc. Cambridge Philos. Soc. 47 (1951), 637–649. MR 43764, DOI 10.1017/S0305004100027092
Trevor Evans, On multiplicative systems defined by generators and relations. II. Monogenic loops, Proc. Cambridge Philos. Soc. 49 (1953), 579–589. MR 57865, DOI 10.1017/S0305004100028772
Trevor Evans, Some connections between residual finiteness, finite embeddability and the word problem, J. London Math. Soc. (2) 1 (1969), 399–403. MR 249344, DOI 10.1112/jlms/s2-1.1.399
Trevor Evans, Identities and relations in commutative Moufang loops, J. Algebra 31 (1974), 508–513. MR 348025, DOI 10.1016/0021-8693(74)90129-X
Trevor Evans, Some solvable word problems, Word problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), Studies in Logic and the Foundations of Mathematics, vol. 95, North-Holland, Amsterdam-New York, 1980, pp. 87–100. MR 579941
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) Studies in Logic and the Foundations of Mathematics, Vol. 80, North-Holland, Amsterdam, 1975, pp. 259–277. MR 0389568
K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. MR 87652, DOI 10.1112/plms/s3-7.1.29
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
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
Marshall Hall Jr., Coset representations in free groups, Trans. Amer. Math. Soc. 67 (1949), 421–432. MR 32642, DOI 10.1090/S0002-9947-1949-0032642-4
P. Hall, Some word-problems, J. London Math. Soc. 33 (1958), 482–496. MR 102540, DOI 10.1112/jlms/s1-33.4.482
G. Higman, Subgroups of finitely presented groups, Proc. Roy. Soc. London Ser. A 262 (1961), 455–475. MR 130286, DOI 10.1098/rspa.1961.0132
J. Kalicki, On comparison of finite algebras, Proc. Amer. Math. Soc. 3 (1952), 36–40. MR 47584, DOI 10.1090/S0002-9939-1952-0047584-3
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
Charles C. Lindner and Trevor Evans, Finite embedding theorems for partial designs and algebras, Séminaire de Mathématiques Supérieures, No. 56 (Été 1971), Les Presses de l’Université de Montréal, Montreal, Que., 1977. MR 0460213
Anatoliĭ Ivanovič Mal′cev, The metamathematics of algebraic systems. Collected papers: 1936–1967, Studies in Logic and the Foundations of Mathematics, Vol. 66, North-Holland Publishing Co., Amsterdam-London, 1971. Translated, edited, and provided with supplementary notes by Benjamin Franklin Wells, III. MR 0349383
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 376323, DOI 10.2307/2271899
Stephen Meskin, A finitely generated residually finite group with an unsolvable word problem, Proc. Amer. Math. Soc. 43 (1974), 8–10. MR 335645, DOI 10.1090/S0002-9939-1974-0335645-5
K. A. Mihaĭlova, The occurrence problem for direct products of groups, Dokl. Akad. Nauk SSSR 119 (1958), 1103–1105 (Russian). MR 0100018
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 210800
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
Morris Orzech and Luis Ribes, Residual finiteness and the Hopf property in rings, J. Algebra 15 (1970), 81–88. MR 255587, DOI 10.1016/0021-8693(70)90087-6
Emil L. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic 12 (1947), 1–11. MR 20527, DOI 10.2307/2267170
Dana Scott, Equationally complete extensions of finite algebras, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 35–38. MR 0082960, DOI 10.1016/S1385-7258(56)50006-6
Philip M. Whitman, Free lattices, Ann. of Math. (2) 42 (1941), 325–330. MR 3614, DOI 10.2307/1969001