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Algebra Logika, 2007, Volume 46, Number 4, Pages 407–427 (Mi al305)  

This article is cited in 1 scientific paper (total in 1 paper)

The quasivariety generated by a torsion-free Abelian-by-finite group

A. I. Budkin


Abstract: Let $L_q(qG)$ be the quasivariety lattice contained in a quasivariety generated by a group $G$. It is proved that if $G$ is a finitely generated torsion-free group in $\mathcal A\mathcal B_{2^n}$ (i.e., $G$ is an extension of an Abelian group by a group of exponent $2^n$), which is a split extension of an Abelian group by a cyclic group, then the lattice $L_q(qG)$ is a finite chain.

Keywords: quasivariety, quasivariety lattice, metabelian group.

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English version:
Algebra and Logic, 2007, 46:4, 219–230

Bibliographic databases:

UDC: 512.54.01
Received: 14.11.2006

Citation: A. I. Budkin, “The quasivariety generated by a torsion-free Abelian-by-finite group”, Algebra Logika, 46:4 (2007), 407–427; Algebra and Logic, 46:4 (2007), 219–230

Citation in format AMSBIB
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\by A.~I.~Budkin
\paper The quasivariety generated by a~torsion-free Abelian-by-finite group
\jour Algebra Logika
\yr 2007
\vol 46
\issue 4
\pages 407--427
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2363551}
\zmath{https://zbmath.org/?q=an:1155.20026}
\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 4
\pages 219--230
\crossref{https://doi.org/10.1007/s10469-007-0021-3}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548747587}


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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. L. Polushin, “A quasivariety lattice of torsion-free soluble groups”, Algebra and Logic, 50:3 (2011), 257–271  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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