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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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543038972624896 |
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| author | Chaynikov, Vladimir |
| author_facet | Chaynikov, Vladimir |
| author_sort | Chaynikov, Vladimir |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:24:09Z |
| 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. |
| first_indexed | 2025-12-02T15:40:36Z |
| format | Article |
| id | admjournalluguniveduua-article-664 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:36Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | hyperbolic groups small cancellation 20F67 20F06 Chaynikov, Vladimir On the generators of the kernels of hyperbolic group presentations |
| title | 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_short | On the generators of the kernels of hyperbolic group presentations |
| title_sort | on the generators of the kernels of hyperbolic group presentations |
| topic | hyperbolic groups small cancellation 20F67 20F06 |
| topic_facet | hyperbolic groups small cancellation 20F67 20F06 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/664 |
| work_keys_str_mv | AT chaynikovvladimir onthegeneratorsofthekernelsofhyperbolicgrouppresentations |