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.

中文翻译：

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关于双曲群的一些商

摘要

本文概括了A. Yu 所著的《定义群中关系的几何》一书中给出的结果。Ol'shanskii 到非循环无挠双曲群的情况。特别地，证明了每个非循环无扭双曲群都有一个非阿贝尔无扭双曲群，其中所有真子群都是循环的，并且它们中的任何两个交集都是非平凡的。