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Sibirsk. Mat. Zh., 2014, Volume 55, Number 6, Pages 1240–1249 (Mi smj2601)  

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

On the closedness of a locally cyclic subgroup in a metabelian group

A. I. Budkin

Altai State University, Barnaul, Russia

Abstract: The dominion of a subgroup $H$ in a group $G$ (in the class of metabelian groups) is the set of all elements $a\in G$ whose images are equal for all pairs of homomorphisms from $G$ into every metabelian group that coincide on $H$. The dominion is a closure operator on the lattice of subgroups of $G$. We study the closed subgroups with respect to the dominion. It is proved that if $G$ is a metabelian group, $H$ is a locally cyclic group, the commutant $G'$ of $G$ is the direct product of its subgroups of the form $H^f$ ($f\in G$), and $G'=H^G\times K$ for a suitable subgroup $K$; then the dominion of $H$ in $G$ coincides with $H$.

Keywords: metabelian group, abelian group, dominion, closed subgroup.

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English version:
Siberian Mathematical Journal, 2014, 55:6, 1009–1016

Bibliographic databases:

UDC: 512.57
Received: 28.02.2014

Citation: A. I. Budkin, “On the closedness of a locally cyclic subgroup in a metabelian group”, Sibirsk. Mat. Zh., 55:6 (2014), 1240–1249; Siberian Math. J., 55:6 (2014), 1009–1016

Citation in format AMSBIB
\Bibitem{Bud14}
\by A.~I.~Budkin
\paper On the closedness of a~locally cyclic subgroup in a~metabelian group
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 6
\pages 1240--1249
\mathnet{http://mi.mathnet.ru/smj2601}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3330032}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 6
\pages 1009--1016
\crossref{https://doi.org/10.1134/S0037446614060044}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000346495200004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919461958}


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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, “Dominions in solvable groups”, Algebra and Logic, 54:5 (2015), 370–379  mathnet  crossref  crossref  mathscinet  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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