Word length in symmetrized presentations of Thompson's group \(F\)

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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Date:2018
Main Authors: Horak, Matthew, Johnson, Alexis, Stonesifer, Amelia
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Thompson's group F
dead ends
diagram group
20F65
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/720
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-720
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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-04-04T10:03:23Z
collection OJS
language English
topic Thompson's group F
dead ends
diagram group
20F65
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 \(F\)
topic_facet Thompson's group F
dead ends
diagram group
20F65
format Article
author Horak, Matthew
Johnson, Alexis
Stonesifer, Amelia
author_facet Horak, Matthew
Johnson, Alexis
Stonesifer, Amelia
author_sort Horak, Matthew
title Word length in symmetrized presentations of Thompson's group \(F\)
title_short 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_sort word length in symmetrized presentations of thompson's group \(f\)
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 \(Z_1\).
publisher Lugansk National Taras Shevchenko University
publishDate 2018
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
first_indexed 2025-12-02T15:40:46Z
last_indexed 2025-12-02T15:40:46Z
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