Geodesic
Wreath Product of O*-Groups that is not in O*
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 453-454

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Modak, S. V. Wreath Product of O*-Groups that is not in O*. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 453-454. doi: 10.4153/CMB-1971-082-2
@article{10_4153_CMB_1971_082_2,
     author = {Modak, S. V.},
     title = {Wreath {Product} of {O*-Groups} that is not in {O*}},
     journal = {Canadian mathematical bulletin},
     pages = {453--454},
     year = {1971},
     volume = {14},
     number = {3},
     doi = {10.4153/CMB-1971-082-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-082-2/}
}
TY  - JOUR
AU  - Modak, S. V.
TI  - Wreath Product of O*-Groups that is not in O*
JO  - Canadian mathematical bulletin
PY  - 1971
SP  - 453
EP  - 454
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-082-2/
DO  - 10.4153/CMB-1971-082-2
ID  - 10_4153_CMB_1971_082_2
ER  - 
%0 Journal Article
%A Modak, S. V.
%T Wreath Product of O*-Groups that is not in O*
%J Canadian mathematical bulletin
%D 1971
%P 453-454
%V 14
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-082-2/
%R 10.4153/CMB-1971-082-2
%F 10_4153_CMB_1971_082_2

[1] 1. Baumslag, G., Wreath products and extensions, Math. Z. 81 (1963), 266-289. Google Scholar

[2] 2. Fuchs, L., On orderable groups, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ. (1965), 89-98. Google Scholar

[3] 3. Fuchs, L., Partially ordered algebraic system, Pergamon Press, Oxford, 1963. Google Scholar

[4] 4. Ohnishi, M., On linearization of ordered groups, Osaka J. Math. 4 (1952), 17-18. Google Scholar

[5] 5. Gupta, N. D. and Rhemtulla, A. H. (to appear). Google Scholar

Cité par Sources :