The largest proper variety of lattice ordered groups
HTML articles powered by AMS MathViewer
- by W. Charles Holland PDF
- Proc. Amer. Math. Soc. 57 (1976), 25-28 Request permission
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
- Charles Holland, The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408. MR 158009
- Jorge Martinez, Varieties of lattice-ordered groups, Math. Z. 137 (1974), 265–284. MR 354483, DOI 10.1007/BF01214370 S. H. McCleary, $o$-primitive ordered permutation groups. I, II, Pacific J. Math. 40 (1972), 349-372; 49 (1973), 431-443. MR 47 #1710.
- Stephen H. McCleary, $o-2$-transitive ordered permutation groups, Pacific J. Math. 49 (1973), 425–429. MR 349525
- Samuel Wolfenstein, Valeurs normales dans un groupe réticulé, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 44 (1968), 337–342 (French, with Italian summary). MR 234887
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 25-28
- MSC: Primary 06A55
- DOI: https://doi.org/10.1090/S0002-9939-1976-0406902-0
- MathSciNet review: 0406902