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Algebra Logika, 2003, Volume 42, Number 5, Pages 542–565 (Mi al43)  

This article is cited in 3 scientific papers (total in 3 papers)

Completion of Linearly Ordered Metabelian Groups

V. V. Bludov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to $\Gamma$-divisible linearly ordered metabelian ones. As a consequence, it is stated that orderable metabelian groups are embedded, with extension of all their linear orders, in $\Gamma$-divisible orderable metabelian groups.

Keywords: linearly ordered metabelian group, $Gamma$-divisible linearly ordered metabelian group, normal convex subgroup.

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English version:
Algebra and Logic, 2003, 42:5, 304–317

Bibliographic databases:

UDC: 512.54
Received: 23.11.2001

Citation: V. V. Bludov, “Completion of Linearly Ordered Metabelian Groups”, Algebra Logika, 42:5 (2003), 542–565; Algebra and Logic, 42:5 (2003), 304–317

Citation in format AMSBIB
\Bibitem{Blu03}
\by V.~V.~Bludov
\paper Completion of Linearly Ordered Metabelian Groups
\jour Algebra Logika
\yr 2003
\vol 42
\issue 5
\pages 542--565
\mathnet{http://mi.mathnet.ru/al43}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025715}
\zmath{https://zbmath.org/?q=an:1067.20054}
\elib{http://elibrary.ru/item.asp?id=8967722}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 5
\pages 304--317
\crossref{https://doi.org/10.1023/A:1025919422046}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22344457267}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Ya. Medvedev, “Soluble Groups and Varieties of $l$-Groups”, Algebra and Logic, 44:3 (2005), 197–204  mathnet  crossref  mathscinet  zmath
    2. V. V. Bludov, “Completion of Linearly Ordered Groups”, Algebra and Logic, 44:6 (2005), 370–380  mathnet  crossref  mathscinet  zmath  elib
    3. V. V. Bludov, V. M. Kopytov, “Extensions of lattice-ordered groups”, Algebra and Logic, 47:5 (2008), 297–303  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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