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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]).

Information

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

References

1. Ault, J. C., Extensions of partial right orders on nilpotent groups, J. London Math. Soc. 2 (1970), 749–752.Google Scholar
2. Baumslag, G., Karass, A., and Solitar, D., Torsion-free groups and amalgamated products, Proc. Amer. Math. Soc. 4 (1970), 688–690.Google Scholar
3. Burns, R. G. and Hale, V. W. D., A note on group rings of certain torsion-free groups, Can. Math. Bull, (to appear).Google Scholar
4. Cohn, P. M., Groups of order automorphisms of ordered sets, Mathematika 4 (1957), 41–50.Google Scholar
5. Paul, Conrad, Right-ordered groups, Michigan Math. J. 6 (1959), 267–275.Google Scholar
6. Fried, E., Representation of partially ordered groups, Acta Sci. Math. (Szeged) 26 (1965), 15–18.Google Scholar
7. Fried, E., Note on the representation of partially ordered groups, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 10 (1967), 85–87.Google Scholar
8. Graham, Higman, The units of group rings, Proc. London Math. Soc. 46 (1940), 231–248.Google Scholar
9. Charles, Holland, The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408.Google Scholar
10. Hollister, H., Doctoral dissertation, University of Michigan, 1965.Google Scholar
11. Karass, A. and Solitar, D., The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227–255.Google Scholar
12. LaGrange, R. H. and Rhemtulla, A. H., A remark on the group rings of order preserving permutation groups, Can. Math. Bull. 11 (1968), 679–680.Google Scholar