Word length in symmetrized presentations of Thompson's group \(F\)
Thompson's groups \(F, T\) and \(Z\) were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generat...
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/720 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543039165562880 |
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| author | Horak, Matthew Johnson, Alexis Stonesifer, Amelia |
| author_facet | Horak, Matthew Johnson, Alexis Stonesifer, Amelia |
| author_sort | Horak, Matthew |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T10:03:23Z |
| description | Thompson's groups \(F, T\) and \(Z\) were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for \(F\), which we denote as \(Z_n\), establish a formula for the word metric with respect to \(Z_1\) and prove that \(F\) has dead ends of depth at least 2 with respect to \(Z_1\). |
| first_indexed | 2025-12-02T15:40:46Z |
| format | Article |
| id | admjournalluguniveduua-article-720 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:46Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7202018-04-04T10:03:23Z Word length in symmetrized presentations of Thompson's group \(F\) Horak, Matthew Johnson, Alexis Stonesifer, Amelia Thompson's group F, dead ends, diagram group 20F65 Thompson's groups \(F, T\) and \(Z\) were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for \(F\), which we denote as \(Z_n\), establish a formula for the word metric with respect to \(Z_1\) and prove that \(F\) has dead ends of depth at least 2 with respect to \(Z_1\). 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/720 Algebra and Discrete Mathematics; Vol 14, No 2 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/720/252 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Thompson's group F dead ends diagram group 20F65 Horak, Matthew Johnson, Alexis Stonesifer, Amelia Word length in symmetrized presentations of Thompson's group \(F\) |
| title | Word length in symmetrized presentations of Thompson's group \(F\) |
| title_full | Word length in symmetrized presentations of Thompson's group \(F\) |
| title_fullStr | Word length in symmetrized presentations of Thompson's group \(F\) |
| title_full_unstemmed | Word length in symmetrized presentations of Thompson's group \(F\) |
| title_short | Word length in symmetrized presentations of Thompson's group \(F\) |
| title_sort | word length in symmetrized presentations of thompson's group \(f\) |
| topic | Thompson's group F dead ends diagram group 20F65 |
| topic_facet | Thompson's group F dead ends diagram group 20F65 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/720 |
| work_keys_str_mv | AT horakmatthew wordlengthinsymmetrizedpresentationsofthompsonsgroupf AT johnsonalexis wordlengthinsymmetrizedpresentationsofthompsonsgroupf AT stonesiferamelia wordlengthinsymmetrizedpresentationsofthompsonsgroupf |