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Right-Ordered Groups

Published online by Cambridge University Press:  20 November 2018

A. H. Rhemtulla
A. H. Rhemtulla*
Affiliation:
University of Alberta, Edmonton, Alberta
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A group G is right-ordered if it can be totally ordered so that for any a, b, c in G, a < b implies that ac < bc. Right-ordered groups, considered as order preserving automorphisms of ordered sets, were studied by Cohn in [4]; but the first systematic study of the structure of these groups was made by Conrad in [5] where he gave several natural characterizations of right-ordered groups. We mention here that the class of right-ordered groups is precisely the subgroup closure of the class of lattice ordered groups (see [6], [7], [9] or [10]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 891 - 895
Copyright
Copyright © Canadian Mathematical Society 1972

References

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