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Wreath Product of O*-Groups that is not in O*

Published online by Cambridge University Press:  20 November 2018

S. V. Modak
S. V. Modak*
Affiliation:
University of Alberta, Edmonton, Alberta
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It is well known that the wreath product of two ordered groups is an ordered group. In [2] Fuchs asks if the same is true for O*-groups. Here we construct an example to show that the wreath product of an infinite cyclic group with a free metabelian group is not an O*-group.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 453 - 454
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Baumslag, G., Wreath products and extensions, Math. Z. 81 (1963), 266-289.Google Scholar
2. Fuchs, L., On orderable groups, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ. (1965), 89-98.Google Scholar
3. Fuchs, L., Partially ordered algebraic system, Pergamon Press, Oxford, 1963.Google Scholar
4. Ohnishi, M., On linearization of ordered groups, Osaka J. Math. 4 (1952), 17-18.Google Scholar
5. Gupta, N. D. and Rhemtulla, A. H. (to appear).Google Scholar