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The word problem for lattice-ordered groups


Authors: A. M. W. Glass and Yuri Gurevich
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
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Abstract: Theorem. There is a finitely generated one relator lattice-ordered group with insoluble (group) word problem.


References [Enhancements On Off] (What's this?)

  • 1. W. W. Boone, The word problem, Ann. of Math. (2) 70 (1959), 207-265. MR 0179237 (31:3485)
  • [1] J. L. Britton, The word problem, Ann. of Math. (2) 77 (1963), 16-32. MR 0168633 (29:5891)
  • [2] A. M. W. Glass, Ordered permutation groups, London Math. Soc. Lecture Notes Ser., No. 55, Cambridge Univ. Press, London and New York, 1981. MR 645351 (83j:06004)
  • [3] -, The word problem for lattice-ordered groups, Proc. Edinburgh Math. Soc. (2) 19 (1975), 217-219. MR 0367071 (51:3313)
  • [4] W. Charles Holland, The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399-408. MR 0158009 (28:1237)
  • [5] W. C. Holland and S. H. McCleary, Solvability of the word problem in free lattice-ordered groups, Houston J. Math. 5 (1979), 99-105. MR 533643 (80f:06018)
  • [6] N. G. Khisamiev, Universal theory of lattice-ordered abelian groups, Algebra i Logika 5 (1966), 71-76. (Russian) MR 0202868 (34:2727)
  • [7] W. Magnus, Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann. 106 (1932), 295-307. MR 1512760
  • [8] S. H. McCleary, A solution of the word problem in free normal valued lattice-ordered groups, Ordered Groups (J. E. Smith, G. O. Kenny and R. N. Ball, eds.) (Proc. Boise State Conf., 1978), Marcel Dekker, New York, 1980, pp. 107-129. MR 601620 (82h:06026)
  • [9] 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 (W. W. Boone, F. B. Cannonito and R. C. Lyndon, eds.) North-Holland, Amsterdam, 1973, pp. 457-478. MR 0396769 (53:629)
  • [10] Julia Robinson, Recursive functions of one variable, Proc. Amer. Math. Soc. 19 (1968), 815-820. MR 0230618 (37:6178)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0712252-3
Article copyright: © Copyright 1983 American Mathematical Society

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