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On the generators of the kernels of hyperbolic group presentations

On the generators of the kernels of hyperbolic group presentations

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...

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Bibliographic Details
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
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Summary: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 [Delz] but the proof seems to require some additional argument. New applications of this theorem are provided.

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