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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 1, Pages 145–163
DOI: https://doi.org/10.1070/IM1990v035n01ABEH000693 (Mi im1275) 		 
This article is cited in 19 scientific papers (total in 19 papers)

On some algorithmic properties of hyperbolic groups

I. G. Lysenok
English version PDF (896 kB) Citations (19)
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DOI: https://doi.org/10.1070/IM1990v035n01ABEH000693
Abstract: For hyperbolic groups the author establishes the solvability of the algorithmic problems of extracting a root of an element, determining the order of an element, membership of a cyclic subgroup, and existence of a solution of an arbitrary quadratic equation. It is proved that every hyperbolic group has a finite presentation for which the word problem can be solved by Dehn's algorithm. The concept of a hyperbolic group was introduced by M. Gromov in a 1986 preprint.
Bibliography: 8 titles.
Received: 04.10.1988
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1989, Volume 53, Issue 4, Pages 814–832
Bibliographic databases:
Document Type: Article
UDC: 512.54.05
MSC: Primary 20F05; Secondary 20F06, 20F32
Language: English
Original paper language: Russian
Citation: I. G. Lysenok, “On some algorithmic properties of hyperbolic groups”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 814–832; Math. USSR-Izv., 35:1 (1990), 145–163
Citation in format AMSBIB
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\by I.~G.~Lysenok
\paper On some algorithmic properties of hyperbolic groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 4
\pages 814--832
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1018749}
\zmath{https://zbmath.org/?q=an:0697.20020|0692.20022}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 145--163
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000693}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1989EB73700007}
Linking options:
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  • https://doi.org/10.1070/IM1990v035n01ABEH000693
  • https://www.mathnet.ru/eng/im/v53/i4/p814
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:491
    Russian version PDF:193
    English version PDF:10
    References:51
    First page:1
     
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