On the generators of the kernels of hyperbolic group presentations

• Date: 2018
• Main Author: Chaynikov, Vladimir
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: hyperbolic groups; small cancellation; 20F67; 20F06
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664
• Journal Title: Algebra and Discrete Mathematics

In this paper we prove that if \(\mathcal{R}\) is a (not necessarily finite) set of words  satisfying certain small cancellation condition in a hyperbolic group \(G\) then the normal closure of \(\mathcal{R}\) is free. This result was first presented (for finite set \(\mathcal{R}\)) by T. Delzant [D...