Extensions of lattice-ordered groups

V. V. Bludov^a, V. M. Kopytov

^a Irkutsk State Pedagogical University

Abstract: 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.

UDC: 512.54

Received: 07.12.2007

 English version: Algebra and Logic, 2008, 47:5, 297–303

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