Geodesic
Ordered Groups Satisfying the Maximal Condition Locally
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 753-758

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

Let denote the class of all (fully) ordered groups satisfying the maximal condition on subgroups, and let denote the class of all locally groups. In this paper we investigate the family of convex subgroups of groups.It is well known (see [1, pp. 51, 54]) that every convex subgroup of an is normal in G, and for any jump D –< C in the family of convex subgroups, [G′, C] ⊆ D. We observe that these properties are also true for any group and record, without proof, the following.THEOREM 1. Any convex subgroup of angroup G is normal in G, and for any jump D –< C in the family of convex subgroups, [G′, C] ⊆ D. 
Hursey, R. J.; Rhemtulla, A. H. Ordered Groups Satisfying the Maximal Condition Locally. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 753-758. doi: 10.4153/CJM-1970-085-7
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