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Algebra Logika, 2012, Volume 51, Number 5, Pages 608–622 (Mi al553)  

This article is cited in 5 scientific papers (total in 5 papers)

Dominions in Abelian subgroups of metabelian groups

A. I. Budkin

Barnaul, Russia

Abstract: It is proved that a suitable free Abelian group of finite rank is not absolutely closed in the class $\mathcal A^2$ of metabelian groups. A condition is specified under which a torsion-free Abelian group is not absolutely closed in $\mathcal A^2$. Also we gain insight into the question when the dominion in $\mathcal A^2$ of the additive group of rational numbers coincides with this subgroup.

Keywords: metabelian group, Abelian subgroup, dominion.

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English version:
Algebra and Logic, 2012, 51:5, 404–414

Bibliographic databases:

UDC: 512.57
Received: 18.06.2012
Revised: 28.09.2012

Citation: A. I. Budkin, “Dominions in Abelian subgroups of metabelian groups”, Algebra Logika, 51:5 (2012), 608–622; Algebra and Logic, 51:5 (2012), 404–414

Citation in format AMSBIB
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\by A.~I.~Budkin
\paper Dominions in Abelian subgroups of metabelian groups
\jour Algebra Logika
\yr 2012
\vol 51
\issue 5
\pages 608--622
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\zmath{https://zbmath.org/?q=an:06138168}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 5
\pages 404--414
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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, “Absolute closedness of torsion-free Abelian groups in the class of metabelian groups”, Algebra and Logic, 53:1 (2014), 9–16  mathnet  crossref  mathscinet  isi
    2. A. I. Budkin, “On the closedness of a locally cyclic subgroup in a metabelian group”, Siberian Math. J., 55:6 (2014), 1009–1016  mathnet  crossref  mathscinet  isi
    3. A. I. Budkin, “Dominions in solvable groups”, Algebra and Logic, 54:5 (2015), 370–379  mathnet  crossref  crossref  mathscinet  isi
    4. A. I. Budkin, “On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups”, Siberian Math. J., 58:6 (2017), 971–982  mathnet  crossref  crossref  isi  elib
    5. A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Siberian Math. J., 59:4 (2018), 598–609  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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