Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 4, Pages 759–772
DOI: https://doi.org/10.17377/smzh.2018.59.403
(Mi smj3008)
 

On dominions of the rationals in nilpotent groups

A. I. Budkin

Altai State University, Barnaul, Russia
References:
Abstract: The dominion of a subgroup $H$ of a group $G$ in a class $M$ is the set of all $a\in G$ that have the same images under every pair of homomorphisms, coinciding on $H$ from $G$ to a group in $M$. A group $H$ is $n$-closed in $M$ if for every group $G=\operatorname{gr}(H,a_1,\dots,a_n)$ in $M$ that includes $H$ 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 rationals is $2$-closed in every quasivariety of torsion-free nilpotent groups of class at most $3$.
Keywords: quasivariety, nilpotent group, additive group of the rationals, dominion, $2$-closed group.
Received: 18.11.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 4, Pages 598–609
DOI: https://doi.org/10.1134/S0037446618040031
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
Citation: A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Sibirsk. Mat. Zh., 59:4 (2018), 759–772; Siberian Math. J., 59:4 (2018), 598–609
Citation in format AMSBIB
\Bibitem{Bud18}
\by A.~I.~Budkin
\paper On dominions of the rationals in nilpotent groups
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 4
\pages 759--772
\mathnet{http://mi.mathnet.ru/smj3008}
\crossref{https://doi.org/10.17377/smzh.2018.59.403}
\elib{https://elibrary.ru/item.asp?id=35722770}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 598--609
\crossref{https://doi.org/10.1134/S0037446618040031}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000443717700003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052987484}
Linking options:
  • https://www.mathnet.ru/eng/smj3008
  • https://www.mathnet.ru/eng/smj/v59/i4/p759
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
    Statistics & downloads:
    Abstract page:253
    Full-text PDF :50
    References:49
    First page:2
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024