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Algebra Logika, 2003, Volume 42, Number 2, Pages 161–181 (Mi al23)  

This article is cited in 2 scientific papers (total in 2 papers)

The Lattice of Quasivarieties of Torsion-Free Metabelian Groups

A. I. Budkin


Abstract: Assume that a quasivariety $\mathcal M$ of groups contains a non-Abelian free metabelian group and a non-Abelian free nilpotent group of class 2. It is proved that the lattice of quasivarieties contained in $\mathcal M$ is infinite and non-modular.

Keywords: quasivariety of torsion-free metabelian groups, lattice, metabelian group, nilpotent group.

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English version:
Algebra and Logic, 2003, 42:2, 92–104

Bibliographic databases:

UDC: 512.54.01
Received: 24.04.2001

Citation: A. I. Budkin, “The Lattice of Quasivarieties of Torsion-Free Metabelian Groups”, Algebra Logika, 42:2 (2003), 161–181; Algebra and Logic, 42:2 (2003), 92–104

Citation in format AMSBIB
\Bibitem{Bud03}
\by A.~I.~Budkin
\paper The Lattice of Quasivarieties of Torsion-Free Metabelian Groups
\jour Algebra Logika
\yr 2003
\vol 42
\issue 2
\pages 161--181
\mathnet{http://mi.mathnet.ru/al23}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2003627}
\zmath{https://zbmath.org/?q=an:1030.08003}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 2
\pages 92--104
\crossref{https://doi.org/10.1023/A:1023398222909}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-23944520755}


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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. A. I. Budkin, “Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups”, Algebra and Logic, 44:4 (2005), 213–218  mathnet  crossref  mathscinet  zmath
    2. A. I. Budkin, “The quasivariety generated by a torsion-free Abelian-by-finite group”, Algebra and Logic, 46:4 (2007), 219–230  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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