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Algebra Logika, 2005, Volume 44, Number 4, Pages 389–398 (Mi al123)  

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

Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups

A. I. Budkin


Abstract: Let $qG$ be a quasivariety generated by a group $G$ and $\mathcal N$ be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose $\mathcal N$ is contained in a quasivariety generated by the following two groups: a free $2$-nilpotent group $F_2(\mathcal N_2)$ of rank 2 and a free metabelian (i. e., with an Abelian commutant) group $F_2(\mathcal A^2)$ of rank 2. It is proved that either $\mathcal N=q F_2(\mathcal N_2)$ or $\mathcal N=q F_2(\mathcal A^2)$ in this instance.

Keywords: quasivariety, free group, metabelian group, 2-nilpotent group

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English version:
Algebra and Logic, 2005, 44:4, 213–218

Bibliographic databases:

UDC: 512.54.01
Received: 28.06.2004

Citation: A. I. Budkin, “Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups”, Algebra Logika, 44:4 (2005), 389–398; Algebra and Logic, 44:4 (2005), 213–218

Citation in format AMSBIB
\Bibitem{Bud05}
\by A.~I.~Budkin
\paper Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups
\jour Algebra Logika
\yr 2005
\vol 44
\issue 4
\pages 389--398
\mathnet{http://mi.mathnet.ru/al123}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2188931}
\zmath{https://zbmath.org/?q=an:1104.08004}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 4
\pages 213--218
\crossref{https://doi.org/10.1007/s10469-005-0022-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-23944483410}


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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, “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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