The word problem for lattice-ordered groups
HTML articles powered by AMS MathViewer
- by A. M. W. Glass and Yuri Gurevich
- Trans. Amer. Math. Soc. 280 (1983), 127-138
- DOI: https://doi.org/10.1090/S0002-9947-1983-0712252-3
- PDF | Request permission
Abstract:
Theorem. There is a finitely generated one relator lattice-ordered group with insoluble (group) word problem.References
- William W. Boone, The word problem, Ann. of Math. (2) 70 (1959), 207–265. MR 179237, DOI 10.2307/1970103
- John L. Britton, The word problem, Ann. of Math. (2) 77 (1963), 16–32. MR 168633, DOI 10.2307/1970200
- A. M. W. Glass, Ordered permutation groups, London Mathematical Society Lecture Note Series, vol. 55, Cambridge University Press, Cambridge-New York, 1981. MR 645351
- A. M. W. Glass, The word problem for lattice ordered groups, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 217–219. MR 367071, DOI 10.1017/S0013091500015479
- Charles Holland, The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408. MR 158009
- W. Charles Holland and Stephen H. McCleary, Solvability of the word problem in free lattice-ordered groups, Houston J. Math. 5 (1979), no. 1, 99–105. MR 533643
- N. G. Hisamiev, Universal theory of lattice-ordered Abelian groups, Algebra i Logika Sem. 5 (1966), no. 3, 71–76 (Russian). MR 0202868
- W. Magnus, Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann. 106 (1932), no. 1, 295–307 (German). MR 1512760, DOI 10.1007/BF01455888
- Stephen H. McCleary, A solution of the word problem in free normal-valued lattice-ordered groups, Ordered groups (Proc. Conf., Boise State Univ., Boise, Idaho, 1978), Lecture Notes in Pure and Appl. Math., vol. 62, Dekker, New York, 1980, pp. 107–129. MR 601620
- Ralph McKenzie and Richard J. Thompson, An elementary construction of unsolvable word problems in group theory, Word problems: decision problems and the Burnside problem in group theory (Conf., Univ. California, Irvine, Calif., 1969; dedicated to Hanna Neumann), Studies in Logic and the Foundations of Math., Vol. 71, North-Holland, Amsterdam, 1973, pp. 457–478. MR 0396769, DOI 10.1016/0003-4916(72)90140-6
- Julia Robinson, Recursive functions of one variable, Proc. Amer. Math. Soc. 19 (1968), 815–820. MR 230618, DOI 10.1090/S0002-9939-1968-0230618-2
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 280 (1983), 127-138
- MSC: Primary 06F15; Secondary 03D40, 20F10
- DOI: https://doi.org/10.1090/S0002-9947-1983-0712252-3
- MathSciNet review: 712252