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Mathematics of the USSR-Sbornik, 1992, Volume 72, Issue 2, Pages 519–541
DOI: https://doi.org/10.1070/SM1992v072n02ABEH002149
(Mi sm1310)
 

This article is cited in 23 scientific papers (total in 23 papers)

Periodic factor of hyperbolic groups

A. Yu. Ol'shanskii

M. V. Lomonosov Moscow State University
References:
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 $G$.)
Received: 17.05.1990
Russian version:
Matematicheskii Sbornik, 1991, Volume 182, Number 4, Pages 543–567
Bibliographic databases:
UDC: 512.543
MSC: Primary 20F50, 20F32, 20E99; Secondary 20F06
Language: English
Original paper language: Russian
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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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..519O}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 2
\pages 519--541
\crossref{https://doi.org/10.1070/SM1992v072n02ABEH002149}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992JT05200015}
Linking options:
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  • https://doi.org/10.1070/SM1992v072n02ABEH002149
  • https://www.mathnet.ru/eng/sm/v182/i4/p543
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1991 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:649
    Russian version PDF:227
    English version PDF:8
    References:61
    First page:1
     
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