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Algebra and Discrete Mathematics, 2011, Volume 11, Issue 2, Pages 18–50 (Mi adm9)  
This article is cited in 3 scientific papers (total in 3 papers)

RESEARCH ARTICLE

On the generators of the kernels of hyperbolic group presentations

Vladimir Chaynikov

Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240
Full-text PDF (427 kB) Citations (3)
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Abstract: In this paper we prove that if R is a (not necessarily finite) set of words satisfying certain small cancellation condition in a hyperbolic group G then the normal closure of R is free. This result was first presented (for finite set R) by T. Delzant [Delz] but the proof seems to require some additional argument. New applications of this theorem are provided.
Keywords: hyperbolic groups, small cancellation.
Received: 12.11.2010
Revised: 12.11.2010
Bibliographic databases:
Document Type: Article
MSC: 20F67, 20F06
Language: English
Citation: Vladimir Chaynikov, “On the generators of the kernels of hyperbolic group presentations”, Algebra Discrete Math., 11:2 (2011), 18–50
Citation in format AMSBIB
\Bibitem{Cha11}
\by Vladimir Chaynikov
\paper On the generators of the kernels of hyperbolic group presentations
\jour Algebra Discrete Math.
\yr 2011
\vol 11
\issue 2
\pages 18--50
\mathnet{http://mi.mathnet.ru/adm9}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2858127}
\zmath{https://zbmath.org/?q=an:06120601}
Linking options:
  • https://www.mathnet.ru/eng/adm9
  • https://www.mathnet.ru/eng/adm/v11/i2/p18
    • This publication is cited in the following 3 articles:
    1. Dahmani F., Guirardel V., Osin D., “Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces”, Mem. Am. Math. Soc., 244:1156 (2017), 1+  crossref  mathscinet  isi  scopus
    2. Cantat S., Lamy S., de Cornulier Y., “Normal Subgroups in the Cremona Group”, Acta Math., 210:1 (2013), 31–94  crossref  mathscinet  zmath  isi  scopus
    3. Kharlampovich O., Myasnikov A., “Definable Sets in a Hyperbolic Group”, Int. J. Algebr. Comput., 23:1 (2013), 91–110  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Algebra and Discrete Mathematics
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    Abstract page:341
    Full-text PDF :148
    References:68
    First page:1
     
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