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Proceedings of the American Mathematical Society

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The largest proper variety of lattice ordered groups

Author: W. Charles Holland
Journal: Proc. Amer. Math. Soc. 57 (1976), 25-28
MSC: Primary 06A55
MathSciNet review: 0406902
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Abstract: If a lattice ordered group $ G$ satisfies any identical relation, other than those satisfied by every lattice ordered group, then $ G$ is normal valued, and hence satisfies the relation $ ab \leqslant {b^2}{a^2}$ for all $ a,b \geqslant e$.

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

  • [1] Charles Holland, The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408. MR 0158009
  • [2] Jorge Martinez, Varieties of lattice-ordered groups, Math. Z. 137 (1974), 265–284. MR 0354483
  • [3] S. H. McCleary, $ o$-primitive ordered permutation groups. I, II, Pacific J. Math. 40 (1972), 349-372; 49 (1973), 431-443. MR 47 #1710.
  • [4] Stephen H. McCleary, 𝑜-2-transitive ordered permutation groups, Pacific J. Math. 49 (1973), 425–429. MR 0349525
  • [5] Samuel Wolfenstein, Valeurs normales dans un groupe réticulé, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 44 (1968), 337–342 (French, with Italian summary). MR 0234887

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Keywords: Lattice ordered group, variety, normal valued
Article copyright: © Copyright 1976 American Mathematical Society