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Atomless Lattice-Ordered Groups

Published online by Cambridge University Press:  20 November 2018

A. M. W. Glass
A. M. W. Glass*
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University Bowling Green, Ohio 43403-0221 U.S.A.
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Abstract

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We show the existence of atomless lattice-ordered groups which have doubly transitive representations. In so doing, we answer a question of M. Giraudet from 1981 [4].

Keywords

06F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 219 - 221
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Droste, M. and Giraudet, M., Embeddings into simple lattice-ordered groups with different first order theories, Forum Math. 1(1989), 315–321.Google Scholar
2. Glass, A. M. W., Ordered Permutation Groups, London Math. Soc. Lecture Notes (55), The University Press, Cambridge, U.K., 1981.Google Scholar
3. Glass, A. M. W. and Holland, W. C., Lattice-ordered Groups: Advances and Techniques, Kluwer Acad. Publ., (eds. A. M. W. Glass and W. C. Holland), Dordrecht, The Netherlands, 1989.Google Scholar
4. Jambu-Giraudet, M., Miscellaneous. In: Ordered Sets, Proc. NATO Advanced Studies Inst., Banff, Canada, 1981, (ed. I. Rival), Reidel Publ. Co., Dordrecht, The Netherlands, 1982, 856–857.Google Scholar
5. Pierce, K. R., Amalgamations of lattice ordered groups, Trans. Amer. Math. Soc. 172(1972), 249–260.Google Scholar