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Mat. Sb., 1991, Volume 182, Number 4, Pages 543–567 (Mi msb1310)  

This article is cited in 19 scientific papers (total in 19 papers)

Periodic factor of hyperbolic groups

A. Yu. Ol'shanskii

M. V. Lomonosov Moscow State University

Abstract: It is proved that for any noncyclic hyperbolic torsion-free group $G$ there exists an integer $n(G)$ such that the factor group $G/G^n$ is infinite for any odd $n\geqslant n(G)$. In addition, $\bigcap_{i=1}^\infty G^i=\{1\}$. (Here $G^i$ is the subgroup generated by the $i$th powers of all elements of the groups $G$.)

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:2, 519–541

Bibliographic databases:

UDC: 512.543
MSC: Primary 20F50, 20F32, 20E99; Secondary 20F06
Received: 17.05.1990

Citation: A. Yu. Ol'shanskii, “Periodic factor of hyperbolic groups”, Mat. Sb., 182:4 (1991), 543–567; Math. USSR-Sb., 72:2 (1992), 519–541

Citation in format AMSBIB
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\by A.~Yu.~Ol'shanskii
\paper Periodic factor of hyperbolic groups
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 4
\pages 543--567
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\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 2
\pages 519--541
\crossref{https://doi.org/10.1070/SM1992v072n02ABEH002149}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Semenov Y., “On Some Quotient Groups of Hyperbolic Groups”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1993, no. 3, 88–90  mathscinet  isi
    2. Gersten S., “Subgroups of Word Hyperbolic Groups in Dimension 2”, J. Lond. Math. Soc.-Second Ser., 54:Part 2 (1996), 261–283  crossref  mathscinet  zmath  isi
    3. Delzant T., “Distinguished Subgroups and Quotients of Hyperbolic Groups”, Duke Math. J., 83:3 (1996), 661–682  crossref  mathscinet  zmath  isi
    4. Ol'shanskii A., “On the Bass-Lubotzky Question About Quotients of Hyperbolic Groups”, J. Algebra, 226:2 (2000), 807–817  crossref  mathscinet  isi
    5. Kapovich I. Wise D., “The Equivalence of Some Residual Properties of Word-Hyperbolic Groups”, J. Algebra, 223:2 (2000), 562–583  crossref  mathscinet  zmath  isi
    6. Arzhantseva G., “On Quasiconvex Subgroups of Word Hyperbolic Groups”, Geod. Dedic., 87:1-3 (2001), 191–208  crossref  mathscinet  zmath  isi
    7. Alperin R., Noskov G., “Nonvanishing of Algebraic Entropy for Geometrically Finite Groups of Isometries of Hadamard Manifolds”, Int. J. Algebr. Comput., 15:5-6, SI (2005), 799–813  crossref  mathscinet  zmath  isi  elib
    8. Minasyan A., “Some Properties of Subsets of Hyperbolic Groups”, Commun. Algebr., 33:3 (2005), 909–935  crossref  mathscinet  zmath  isi
    9. Minasyan A., “On Residualizing Homomorphisms Preserving Quasiconvexity”, Commun. Algebr., 33:7 (2005), 2423–2463  crossref  mathscinet  zmath  isi
    10. Ashot Minasyan, “On residual properties of word hyperbolic groups”, jgth, 9:5 (2006), 695  crossref  mathscinet  zmath  isi
    11. Arzhantseva G., “A Dichotomy for Finitely Generated Subgroups of Word Hyperbolic Groups”, Topological and Asymptotic Aspects of Group Theory, Contemporary Mathematics Series, 394, eds. Grigorchuk R., Mihalik M., Sapir M., Suik Z., Amer Mathematical Soc, 2006, 1–10  crossref  mathscinet  zmath  isi
    12. Denis V. Osin, “Peripheral fillings of relatively hyperbolic groups”, Invent math, 167:2 (2007), 295  crossref  mathscinet  zmath  isi  elib
    13. Abderezak Ould Houcine, “On superstable CSA-groups”, Annals of Pure and Applied Logic, 154:1 (2008), 1  crossref
    14. Gopal Prasad, Andrei S. Rapinchuk, “Weakly commensurable arithmetic groups and isospectral locally symmetric spaces”, Publ math IHES, 2009  crossref  mathscinet  zmath  isi
    15. A. V. Kvaschuk, A. G. Myasnikov, D. E. Serbin, “Pregroups and the big powers condition”, Algebra and Logic, 48:3 (2009), 193–213  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    16. 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
    17. Mark Sapir, “Asymptotic invariants, complexity of groups and related problems”, Bull. Math. Sci, 2011  crossref
    18. Coulon R., “Growth of Periodic Quotients of Hyperbolic Groups”, Algebr. Geom. Topol., 13:6 (2013), 3111–3133  crossref  isi
    19. 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
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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