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Right-Ordered Polycyclic Groups

Published online by Cambridge University Press:  20 November 2018

Roberta Botto Mura
Roberta Botto Mura*
Affiliation:
University of Alberta, Edmonton, Canada
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One of the features that make right-ordered groups harder to investigate than ordered groups is that their system of convex subgroups may fail to have the following property:

(*) if C and C’ are convex subgroups of G and C’ covers C, then C is normal in C’ and C’/C is order-isomorphic to a subgroup of the naturally ordered additive group of real numbers.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 175 - 178
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Ault, J. C., Right-ordered locally nilpotentgroups, J. London Math. Soc. (2), 4 (1972), 662-666.Google Scholar
2. Conrad, P., Right-ordered groups, Michigan Math. J., 6, N.3, 1959, 267-275.Google Scholar
3. Fuchs, L., On order able groups, in Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ., Canberra, August 1965, pp. 89-98. Gordon and Breach Science Publishers, Inc. 1967.Google Scholar
4. Hursey, R. J. Jr and Rhemtulla, A. H., Ordered groups satisfying the maximal condition locally, Can. J. Math., Vol. XXII (1970), 753-758.Google Scholar
5. Oltikar, B. C., Right cyclically ordered groups. To appear.Google Scholar
6. Rhemtulla, A. H., Right-ordered groups, Can. J. Math., Vol. XXIV (1972), 891-895.Google Scholar