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Sibirsk. Mat. Zh., 2010, Volume 51, Number 3, Pages 498–505 (Mi smj2101)  

This article is cited in 9 scientific papers (total in 9 papers)

Dominions in quasivarieties of metabelian groups

A. I. Budkin

Altai State University, Barnaul

Abstract: The dominion of a subgroup $H$ of a group $A$ in a quasivariety $\mathscr M$ is the set of all $a\in A$ with equal images under all pairs of homomorphisms from $A$ into every group in $\mathscr M$ which coincide on $H$. The concept of dominion provides some closure operator on the lattice of subgroups of a given group. We study the closed subgroups with respect to this operator. We find a condition for the dominion of a divisible subgroup in quasivarieties of metabelian groups to coincide with the subgroup.

Keywords: quasivariety, metabelian group, dominion, $n$-closed subgroup, closure operator.

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English version:
Siberian Mathematical Journal, 2010, 51:3, 396–401

Bibliographic databases:

UDC: 512.57
Received: 04.04.2009

Citation: A. I. Budkin, “Dominions in quasivarieties of metabelian groups”, Sibirsk. Mat. Zh., 51:3 (2010), 498–505; Siberian Math. J., 51:3 (2010), 396–401

Citation in format AMSBIB
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\by A.~I.~Budkin
\paper Dominions in quasivarieties of metabelian groups
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
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\pages 498--505
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\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 3
\pages 396--401
\crossref{https://doi.org/10.1007/s11202-010-0040-5}
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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. Budkin A.I., “O dominione polnoi podgruppy metabelevoi gruppy”, Izv. Altaiskogo gos. un-ta, 2010, no. 1-2, 15–19  elib
    2. Budkin A.I., “O dominionakh konechnykh podgrupp”, Izvestiya Altaiskogo gosudarstvennogo universiteta, 2011, no. 1-2, 15–18  elib
    3. A. I. Budkin, “Dominions in Abelian subgroups of metabelian groups”, Algebra and Logic, 51:5 (2012), 404–414  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. 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
    6. S. A. Shakhova, “Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups”, Math. Notes, 97:6 (2015), 946–950  mathnet  crossref  crossref  mathscinet  isi  elib
    7. A. I. Budkin, “Dominions in solvable groups”, Algebra and Logic, 54:5 (2015), 370–379  mathnet  crossref  crossref  mathscinet  isi
    8. 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
    9. A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Siberian Math. J., 59:4 (2018), 598–609  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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