On Some Quotients of Hyperbolic Groups

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 quoti...

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Bibliographic Details
Published in:Mathematical Notes 2023-08, Vol.114 (1-2), p.99-107
Main Author: Kulikova, O. V.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Mathematics
Mathematics and Statistics
Quotients
Subgroups
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Summary: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.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623070106