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Matematicheskie Zametki, 2023, Volume 114, Issue 1, Pages 121–132
DOI: https://doi.org/10.4213/mzm13688 (Mi mzm13688) 		 
On Some Quotients of Hyperbolic Groups

O. V. Kulikovaab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.4213/mzm13688
Abstract: This paper presents generalizations of results given in the book Geometry of Defining Relations in Groups by A. Yu. Ol'shanskii to the case of noncyclic torsion-free hyperbolic groups. In particular, it is proved that every noncyclic torsion-free hyperbolic group has a non-Abelian torsion-free quotient in which all proper subgroups are cyclic and the intersection of any two of them is nontrivial.
Keywords: torsion-free hyperbolic group, quotient group.
Funding agency Grant number
Russian Science Foundation 22-11-00075
This work was financially supported by the Russian Science Foundation, project no. 22-11-00075, https://rscf.ru/en/project/22-11-00075/.
Received: 12.08.2022
English version:
Mathematical Notes, 2023, Volume 114, Issue 1, Pages 99–107
DOI: https://doi.org/10.1134/S0001434623070106
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 20F05,20F65, 20F67
Language: Russian
Citation: O. V. Kulikova, “On Some Quotients of Hyperbolic Groups”, Mat. Zametki, 114:1 (2023), 121–132; Math. Notes, 114:1 (2023), 99–107
Citation in format AMSBIB
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\pages 121--132
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\transl
\jour Math. Notes
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\pages 99--107
\crossref{https://doi.org/10.1134/S0001434623070106}
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