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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 814–832 (Mi izv1275)  

This article is cited in 9 scientific papers (total in 9 papers)

On some algorithmic properties of hyperbolic groups

I. G. Lysenok


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.

Full text: PDF file (1832 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 145–163

Bibliographic databases:

UDC: 512.54.05
MSC: Primary 20F05; Secondary 20F06, 20F32
Received: 04.10.1988

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://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989EB73700007}


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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. N. B. Bezverkhnyaya, “Hyperbolicity of some 2-generator groups with one defining condition”, Discrete Math. Appl., 12:4 (2002), 357–373  mathnet  crossref  mathscinet  zmath
    2. E. G. Kukina, V. A. Roman'kov, “Subquadratic growth of the averaged Dehn function for free Abelian groups”, Siberian Math. J., 44:4 (2003), 605–610  mathnet  crossref  mathscinet  zmath  isi
    3. Leo P Comerford, Charles C Edmunds, “The two variable substitution problem for free products of groups”, jgth, 11:1 (2008), 141  crossref  mathscinet  zmath  isi
    4. François Dahmani, Daniel Groves, “The isomorphism problem for toral relatively hyperbolic groups”, Publ.math.IHES, 107:1 (2008), 211  crossref
    5. V. S. Atabekyan, “Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period”, Math. Notes, 85:4 (2009), 496–502  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. VOLKER DIEKERT, ALEXEI MYASNIKOV, “GROUP EXTENSIONS OVER INFINITE WORDS”, Int. J. Found. Comput. Sci, 23:05 (2012), 1001  crossref
    8. S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71  mathnet  crossref  crossref  isi  elib
    9. I. V. Dobrynina, “O normalizatorakh v nekotorykh gruppakh Kokstera”, Chebyshevskii sb., 17:2 (2016), 113–127  mathnet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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