Geodesic
Normal relatively convex subgroups of solvable orderable groups
Algebra i logika, Tome 48 (2009) no. 3, pp. 291-308.

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Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed than it is precisely the class of solvable orderable groups which are locally of finite (Mal'tsev) rank. A criterion for an orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an orderable solvable group $G$ of length three with periodic $G/G'$ and of an orderable solvable group of length four with only one proper normal relatively convex subgroup are constructed.
Keywords: ordered group, convex subgroup.
Mots-clés : solvable group 
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V. V. Bludov; V. M. Kopytov; A. H. Rhemtulla. Normal relatively convex subgroups of solvable orderable groups. Algebra i logika, Tome 48 (2009) no. 3, pp. 291-308. http://geodesic.mathdoc.fr/item/AL_2009_48_3_a0/

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