RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra Logika, 2005, Volume 44, Number 3, Pages 355–367 (Mi al118)  

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

Soluble Groups and Varieties of $l$-Groups

N. Ya. Medvedev


Abstract: A sufficient condition is given under which factors of a system of normal convex subgroups of a linearly ordered (l. o. ) group are Abelian. Also, a sufficient condition is specified subject to which factors of a system of normal convex subgroups of an l. o. group are contained in a group variety $\mathcal V$. In particular, for every soluble l. o. group $G$ of solubility index $n$, $n\geqslant2$, factors of a system of normal convex subgroups are soluble l. o. groups of solubility index at most $n-1$. It is proved that the variety $\mathcal R$ of all lattice-ordered groups, approximable by linearly ordered groups, does not coincide with a variety generated by all soluble l. o. groups. It is shown that if $\mathcal V$ is any $o$-approximable variety of $l$-groups, and if every identity in the group signature is not identically true in $\mathcal V$, then $\mathcal V$ contains free l. o. groups.

Keywords: variety of $l$-groups, soluble group

Full text: PDF file (190 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2005, 44:3, 197–204

Bibliographic databases:

UDC: 512.545
Received: 27.04.2004
Revised: 01.07.2004

Citation: N. Ya. Medvedev, “Soluble Groups and Varieties of $l$-Groups”, Algebra Logika, 44:3 (2005), 355–367; Algebra and Logic, 44:3 (2005), 197–204

Citation in format AMSBIB
\Bibitem{Med05}
\by N.~Ya.~Medvedev
\paper Soluble Groups and Varieties of $l$-Groups
\jour Algebra Logika
\yr 2005
\vol 44
\issue 3
\pages 355--367
\mathnet{http://mi.mathnet.ru/al118}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2170691}
\zmath{https://zbmath.org/?q=an:1101.06011}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 3
\pages 197--204
\crossref{https://doi.org/10.1007/s10469-005-0020-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22344452213}


Linking options:
  • http://mi.mathnet.ru/eng/al118
  • http://mi.mathnet.ru/eng/al/v44/i3/p355

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. W. Glass, N. Ya. Medvedev, “Unilateral $o$-Groups”, Algebra and Logic, 45:1 (2006), 12–16  mathnet  crossref  mathscinet  zmath
    2. V. V. Bludov, V. M. Kopytov, “Extensions of lattice-ordered groups”, Algebra and Logic, 47:5 (2008), 297–303  mathnet  crossref  mathscinet  zmath  isi
    3. V. V. Bludov, V. M. Kopytov, A. H. Rhemtulla, “Normal relatively convex subgroups of solvable orderable groups”, Algebra and Logic, 48:3 (2009), 163–172  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:205
    Full text:60
    References:30
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019