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Sibirsk. Mat. Zh., 2017, Volume 58, Number 6, Pages 1252–1266 (Mi smj2935)  

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

On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups

A. I. Budkin

Altai State University, Barnaul, Russia

Abstract: The dominion of a subgroup $H$ of a group $G$ in a class $M$ is the set of all elements $a\in G$ that have equal images under every pair of homomorphisms from $G$ to a group of $M$ coinciding on $H$. A group $H$ is said to be $n$-closed in $M$ if for every group $G=\operatorname{gr}(H,a_1,…,a_n)$ of $M$ that contains $H$ and is generated modulo $H$ by some $n$ elements, the dominion of $H$ in $G$ (in $M$) is equal to $H$. We prove that the additive group of the rational numbers is $2$-closed in every quasivariety $M$ of torsion-free nilpotent groups of class at most $3$ whenever every $2$-generated group of $M$ is relatively free.

Keywords: quasivariety, nilpotent group, additive group of the rational numbers, dominion, $2$-closed group.

DOI: https://doi.org/10.17377/smzh.2017.58.606

Full text: PDF file (360 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:6, 971–982

Bibliographic databases:

UDC: 512.57
Received: 09.12.2016

Citation: A. I. Budkin, “On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups”, Sibirsk. Mat. Zh., 58:6 (2017), 1252–1266; Siberian Math. J., 58:6 (2017), 971–982

Citation in format AMSBIB
\Bibitem{Bud17}
\by A.~I.~Budkin
\paper On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 6
\pages 1252--1266
\mathnet{http://mi.mathnet.ru/smj2935}
\crossref{https://doi.org/10.17377/smzh.2017.58.606}
\elib{http://elibrary.ru/item.asp?id=30556273}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 6
\pages 971--982
\crossref{https://doi.org/10.1134/S0037446617060064}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425153500006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042144721}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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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