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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References
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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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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