On Some Quotients of Hyperbolic Groups

O. V. Kulikova<sup>ab

a</sup> Lomonosov Moscow State University
^b Moscow Center for Fundamental and Applied Mathematics

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.

UDC: 517.98

MSC: 20F05,20F65, 20F67

Received: 12.08.2022

DOI: 10.4213/mzm13688

 English version: Mathematical Notes, 2023, 114:1, 99–107

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