Geodesic
Extensions of lattice-ordered groups
Algebra i logika, Tome 47 (2008) no. 5, pp. 529-540.

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A number of conditions are specified which are sufficient for totally ordered groups with polycyclic factor group to contain a finite normal series of convex subgroups whose factors possess good enough properties. In any case studying such totally ordered groups is reduced to treating extensions of these groups as well as their virtually $o$-equivalent extensions. The concept of a virtually $o$-equivalent extension is a particular case of the notion of an Archimedean extension.
Keywords: totally ordered group, virtually $o$-equivalent extension, Archimedean extension. 
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V. V. Bludov; V. M. Kopytov. Extensions of lattice-ordered groups. Algebra i logika, Tome 47 (2008) no. 5, pp. 529-540. http://geodesic.mathdoc.fr/item/AL_2008_47_5_a0/

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