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On Some Quotients of Hyperbolic Groups

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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.

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Acknowledgments

The author thanks A. Yu. Ol’shanskii for setting the problem, suggesting a method for its solution, and useful discussions.

Funding

This work was financially supported by the Russian Science Foundation, project no. 22-11-00075, https://rscf.ru/en/project/22-11-00075/.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    O. V. Kulikova

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    O. V. Kulikova

Authors
  1. O. V. Kulikova
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Correspondence to O. V. Kulikova.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 121–132 https://doi.org/10.4213/mzm13688.

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Kulikova, O.V. On Some Quotients of Hyperbolic Groups. Math Notes 114, 99–107 (2023). https://doi.org/10.1134/S0001434623070106

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  • DOI: https://doi.org/10.1134/S0001434623070106

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