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Algebra Logika, 2001, Volume 40, Number 3, Pages 251–261 (Mi al219)  

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

Generating Elements for Groups of the Form $F/R'$

Ch. K. Guptaa, E. I. Timoshenko

a University of Manitoba

Abstract: Necessary and sufficient conditions are specified for a group of a specified type to be generated by its given elements ($F$ is a free product). Using these conditions (and relying essentially on the Shmel'kin embedding), we establish the criterion of being primitive for metabelian products of Abelian groups. A result by Birman and the primitivity criterion for free metabelian groups are generalized.

Keywords: metabelian products of Abelian groups, free metabelian group, generator

Full text: PDF file (932 kB)

English version:
Algebra and Logic, 2001, 40:3, 137–143

Bibliographic databases:

UDC: 512.5
Received: 18.11.1999

Citation: Ch. K. Gupta, E. I. Timoshenko, “Generating Elements for Groups of the Form $F/R'$”, Algebra Logika, 40:3 (2001), 251–261; Algebra and Logic, 40:3 (2001), 137–143

Citation in format AMSBIB
\Bibitem{GupTim01}
\by Ch.~K.~Gupta, E.~I.~Timoshenko
\paper Generating Elements for Groups of the Form $F/R'$
\jour Algebra Logika
\yr 2001
\vol 40
\issue 3
\pages 251--261
\mathnet{http://mi.mathnet.ru/al219}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857882}
\zmath{https://zbmath.org/?q=an:1003.20030}
\transl
\jour Algebra and Logic
\yr 2001
\vol 40
\issue 3
\pages 137--143
\crossref{https://doi.org/10.1023/A:1010266417056}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249088176}


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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. Ch. K. Gupta, E. I. Timoshenko, “Criterion for Invertibility of Endomorphisms and Test Rank of Metabelian Products of Abelian Groups”, Algebra and Logic, 43:5 (2004), 316–326  mathnet  crossref  mathscinet  zmath  elib  elib
    2. E. I. Timoshenko, “On a Presentation of the Automorphism Group of a Partially Commutative Metabelian Group”, Math. Notes, 97:2 (2015), 275–283  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. F. Krasnikov, “Generating elements for groups and Lie algebras of the form $F/[N,N]$”, J. Math. Sci., 215:4 (2016), 517–528  mathnet  crossref  crossref
  • Алгебра и логика Algebra and Logic
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