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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Logika, 2014, Volume 53, Number 1, Pages 15–25 (Mi al621)  

This article is cited in 3 scientific papers (total in 3 papers)

Absolute closedness of torsion-free Abelian groups in the class of metabelian groups

A. I. Budkin

Pavlovskii road, 60a-168, Barnaul, 656064, Russia

Abstract: The dominion of a subgroup $H$ of a group $G$ in a class $M$ is the set of all elements $a\in G$ whose images are equal for all pairs of homomorphisms from $G$ to each group in $M$ that coincide on $H$. A group $H$ is absolutely closed in a class $M$ if, for any group $G$ in $M$, every inclusion $H\le G$ implies that the dominion of $H$ in $G$ (in $M$) coincides with $H$.
We deal with dominions in torsion-free Abelian subgroups of metabelian groups. It is proved that every nontrivial torsion-free Abelian subgroup is not absolutely closed in the class of metabelian groups. It is stated that if a torsion-free subgroup $H$ of a metabelian group $G$ and the commutator subgroup $G'$ have trivial intersection, then the dominion of $H$ in $G$ (in the class of metabelian groups) coincides with $H$.

Keywords: quasivariety, metabelian group, Abelian group, dominion, absolutely closed subgroup.

Full text: PDF file (172 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2014, 53:1, 9–16

Bibliographic databases:

UDC: 512.57
Received: 02.12.2013
Revised: 22.01.2014

Citation: A. I. Budkin, “Absolute closedness of torsion-free Abelian groups in the class of metabelian groups”, Algebra Logika, 53:1 (2014), 15–25; Algebra and Logic, 53:1 (2014), 9–16

Citation in format AMSBIB
\Bibitem{Bud14}
\by A.~I.~Budkin
\paper Absolute closedness of torsion-free Abelian groups in the class of metabelian groups
\jour Algebra Logika
\yr 2014
\vol 53
\issue 1
\pages 15--25
\mathnet{http://mi.mathnet.ru/al621}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237620}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 1
\pages 9--16
\crossref{https://doi.org/10.1007/s10469-014-9267-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000337279400002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902344958}


Linking options:
  • http://mi.mathnet.ru/eng/al621
  • http://mi.mathnet.ru/eng/al/v53/i1/p15

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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
    2. 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
    3. 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
    Number of views:
    This page:177
    Full text:34
    References:67
    First page:42

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019