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Compatible Tight Riesz Orders

Published online by Cambridge University Press:  20 November 2018

A. M. W. Glass
A. M. W. Glass*
Affiliation:
Bowling Green State University, Bowling Green, Ohio
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N. R. Reilly has obtained an algebraic characterization of the compatible tight Riesz orders that can be supported by certain partially ordered groups [13; 14]. The purpose of this paper is to give a “geometric“ characterization by the use of ordered permutation groups. Our restrictions on the partially ordered groups will likewise be geometric rather than algebraic. Davis and Bolz [3] have done some work on groups of all order-preserving permutations of a totally ordered field; from our more general theorems, we will be able to recapture their results.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 186 - 200
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Ball, R. N., Full convex l-subgroups of a lattice-ordered group, Ph.D. thesis, University of Wisconsin, Madison, 1974.Google Scholar
2. Conrad, P. F., Lattice-ordered groups, Lecture Notes, Tulane University, 1970.Google Scholar
3. Davis, G. and Bolz, E., Compatible tight Riesz orders on ordered permutation groups, to appear, J. Australian Math. Soc.Google Scholar
4. Glass, A. M. W., Ordered-permutation groups, Bowling Green State University, 1976.Google Scholar
5. Holland, W. C., The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408.Google Scholar
6. Holland, W. C., Transitive lattice-ordered permutation groups, Math. Z. 87 (1965), 420–433.Google Scholar
7. Holland, W. C., Aciass of simple lattice-ordered groups, Proc. Amer. Math. Soc. 16 (1965), 326–329.Google Scholar
8. Holland, W. C. and McCleary, S. H., Wreath products of ordered permutation groups, Pacific J. Math. 31 (1969), 703–716.Google Scholar
9. McCleary, S. H., o-primitive ordered permutation groups, Pacific J. Math. 40 (1972), 349–372.Google Scholar
10. McCleary, S. H., o-primitive ordered permutation groups II, Pacific J. Math. 49 (1973), 431–443.Google Scholar
11. McCleary, S. H., The structure of intransitive ordered permutation groups, to appear, Algebra Universalis.Google Scholar
12. Ohkuma, T., Sur quelques ensembles ordonné linéairement, Fund. Math. 43 (1954), 326–337.Google Scholar
13. Reilly, N. R., Compatible tight Riesz orders and prime subgroups, Glasgow Math. J. 14 (1973), 145–160.Google Scholar
14. Reilly, N. R., Representations of ordered groups with compatible tight Riesz orders, to appear.Google Scholar
15. Wirth, A., Compatible tight Riesz orders, J. Australian Math. Soc. 15 (1973), 105–111.Google Scholar