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Algebra Logika, 2007, Volume 46, Number 3, Pages 290–298 (Mi al298)  

This article is cited in 5 scientific papers (total in 5 papers)

Free subgroups of one-relator relative presentations

A. A. Klyachko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Suppose that $G$ is a non-trivial torsion-free group and $w$ is a word over the alphabet $G\cup\{x^{\pm1}_1,…,x^{\pm1}_n\}$. It is proved that, for $n\geqslant2$, the group $\widetilde G=\langle G,x_1,x_2,…,x_n | w = 1\rangle$ always contains a non-Abelian free subgroup. For $n=1$, the question whether there exist non-Abelian free subgroups in $\widetilde G$ is amply settled for the unimodular case (i.e., where the exponent sum of $x_1$ in $w$ is one). Some generalizations of these results are discussed.

Keywords: relative presentations, one-relator groups, free subgroups.

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English version:
Algebra and Logic, 2007, 46:3, 158–162

Bibliographic databases:

UDC: 512.543.7+512.543.16
Received: 17.11.2005

Citation: A. A. Klyachko, “Free subgroups of one-relator relative presentations”, Algebra Logika, 46:3 (2007), 290–298; Algebra and Logic, 46:3 (2007), 158–162

Citation in format AMSBIB
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\by A.~A.~Klyachko
\paper Free subgroups of one-relator relative presentations
\jour Algebra Logika
\yr 2007
\vol 46
\issue 3
\pages 290--298
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\zmath{https://zbmath.org/?q=an:1155.20031}
\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 3
\pages 158--162
\crossref{https://doi.org/10.1007/s10469-007-0015-1}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548221403}


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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. Ant. A. Klyachko, “$SQ$-universality of one-relator relative presentations”, Sb. Math., 197:10 (2006), 1489–1508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Klyachko A.A., “The structure of one-relator relative presentations and their centres”, J. Group Theory, 12:6 (2009), 923–947  crossref  mathscinet  zmath  isi  elib  scopus
    3. Giang L.T., “The relative hyperbolicity of one-relator relative presentations”, J. Group Theory, 12:6 (2009), 949–959  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Klyachko A.A., Lurye D.E., “Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator”, J Pure Appl Algebra, 216:3 (2012), 524–534  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ivanov S.V., Klyachko A.A., “Quasiperiodic and Mixed Commutator Factorizations in Free Products of Groups”, Bull. London Math. Soc., 50:5 (2018), 832–844  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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