Some $l$-simple pathological lattice-ordered groups
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- by A. M. W. Glass and Stephen H. McCleary PDF
- Proc. Amer. Math. Soc. 57 (1976), 221-226 Request permission
Abstract:
The purpose of this note is to explore two recently discovered lattice-ordered groups, and to establish that they are $l$-simple, i.e., have no proper $l$-ideals. These groups are “pathologically $o-2$-transitive” ordered permutation groups acting on the real line. The two groups exhibit even nastier properties than previous pathological groups, and serve as counterex-amples to several conjectures about $l$-groups.References
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Richard Ball, Full convex $l$-subgroups of a lattice ordered group, Ph. D. Dissertation, University of Wisconsin, Madison, Wis., 1974.
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 221-226
- MSC: Primary 06A55
- DOI: https://doi.org/10.1090/S0002-9939-1976-0404089-1
- MathSciNet review: 0404089