Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-09T18:35:44.445Z Has data issue: false hasContentIssue false
  • English
  • Français

Right Cyclically Ordered Groups(1)

Published online by Cambridge University Press:  20 November 2018

B. C. Oltikar
B. C. Oltikar*
Affiliation:
Department of Mathematics Carleton University, Ottawa, Ontario Canada K1S 5B6
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper presents a study of right cyclically ordered groups (RCO-groups) and their relation to right ordered groups (RO-groups). Cyclically ordered groups (CO-groups) and their connection with ordered groups (O-groups) have been studied by Rieger in [7] and by Swierczkowski in [8]. While some of the properties of RCO-groups are analogous to the corresponding ones for COgroups, there are interesting exceptions.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 67 - 70
Copyright
Copyright © Canadian Mathematical Society 1980

Footnotes

Current Address: Department of Mathematics, University of Puerto Rico Mayagüez Campus, Mayagüez, Puerto Rico 00708

(1)

This paper is a part of the Author's M.Sc. thesis written at the University of Alberta under the supervision of Prof. A. H. Rhemtulla. The author wishes to thank Prof. A. H. Rhemtulla for suggesting the problem and for his guidance.

References

1. Baumslag, G., Karrass, A. and Solitar, D., Torsion-free Groups and Amalgamated Products, Proc. Amer. Math. Soc. 24 (1970), 688-690.Google Scholar
2. Paul, Conrad, Right-Ordered Groups, Michigan Math. J., 6 (1959), 267-275.Google Scholar
3. Fuchs, L., Partially Ordered Algebraic Systems, Pergamon Press, 1963.Google Scholar
4. Karrass, A. and Solitar, D., The subgroups of a Free Pro Product of Two Groups with an Amalgamated Subgroup, Trans. Amer. Math. Soc. 150 (1970), 227-255.Google Scholar
5. Mura, Roberta B. and Rhemtulla, A. H., Orderable Groups, Printed: Lecture Notes in Pure & Applied Algebra, Vol. 27, Marcel Dekker.Google Scholar
6. Rhemtulla, A. H., Right Ordered Groups, Can. J. Math. 24 (1972), 891-895.Google Scholar
7. Riger, L., On the Ordered and Cyclically Ordered Groups, I?III, Vestnik Krai. Ceske Spol. Nauk, (1946) No. 6, 1-31; (1947), No. 1, 1-33; (1948) No. 1, 1-26.Google Scholar
8. Swierczkowski, S., On Cyclically Ordered Groups, Fund. Math., 47 (1959), 161-166.Google Scholar
9. Zeleva, S. D., Cyclically Ordered Groups, Siberian Math. J., 17 (1976), 773-777.Google Scholar