Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 0404089
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A55

Retrieve articles in all journals with MSC: 06A55

Additional Information

Keywords: Lattice-ordered group, $ l$-simple, ordered permutation group
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society