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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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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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spelling oai:ojs.admjournal.luguniv.edu.ua:article-6642018-04-04T09:24:09Z On the generators of the kernels of hyperbolic group presentations Chaynikov, Vladimir hyperbolic groups, small cancellation 20F67, 20F06 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664 Algebra and Discrete Mathematics; Vol 11, No 2 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664/198 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic hyperbolic groups
small cancellation
20F67
20F06
spellingShingle hyperbolic groups
small cancellation
20F67
20F06
Chaynikov, Vladimir
On the generators of the kernels of hyperbolic group presentations
topic_facet hyperbolic groups
small cancellation
20F67
20F06
format Article
author Chaynikov, Vladimir
author_facet Chaynikov, Vladimir
author_sort Chaynikov, Vladimir
title On the generators of the kernels of hyperbolic group presentations
title_short On the generators of the kernels of hyperbolic group presentations
title_full On the generators of the kernels of hyperbolic group presentations
title_fullStr On the generators of the kernels of hyperbolic group presentations
title_full_unstemmed On the generators of the kernels of hyperbolic group presentations
title_sort on the generators of the kernels of hyperbolic group presentations
description 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.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664
work_keys_str_mv AT chaynikovvladimir onthegeneratorsofthekernelsofhyperbolicgrouppresentations
first_indexed 2024-04-12T06:25:46Z
last_indexed 2024-04-12T06:25:46Z
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