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Proceedings of the American Mathematical Society

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Some $ l$-simple pathological lattice-ordered groups


Authors: A. M. W. Glass and Stephen H. McCleary
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0404089-1
Keywords: Lattice-ordered group, $ l$-simple, ordered permutation group
Article copyright: © Copyright 1976 American Mathematical Society