On the Tits alternative for some generalized triangle groups

On the Tits alternative for some generalized triangle groups

One says that the Tits alternative holds for a finitely generated group \(\Gamma\) if \(\Gamma\) contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized triangle groups \(T(k,l,m,R)=\langle...

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Date:2018
Main Authors: Beniash-Kryvets, Valery, Barkovich, Oxana
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Tits alternative
generalized triangle group
free subgroup
20E06
20E07
20H10
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/988
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-988
record_format ojs
spelling admjournalluguniveduua-article-9882018-05-15T05:12:44Z On the Tits alternative for some generalized triangle groups Beniash-Kryvets, Valery Barkovich, Oxana Tits alternative, generalized triangle group, free subgroup 20E06, 20E07, 20H10 One says that the Tits alternative holds for a finitely generated group \(\Gamma\) if \(\Gamma\) contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized triangle groups \(T(k,l,m,R)=\langle a,b; a^k=b^l=R^m(a,b)=1\rangle\). In the paper Rosenberger's conjecture is proved for groups \(T(2,l,2,R)\) with \(l=6,12,30,60\) and some special groups \(T(3,4,2,R)\). Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/988 Algebra and Discrete Mathematics; Vol 3, No 2 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/988/517 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-05-15T05:12:44Z
collection OJS
language English
topic Tits alternative
generalized triangle group
free subgroup
20E06
20E07
20H10
spellingShingle Tits alternative
generalized triangle group
free subgroup
20E06
20E07
20H10
Beniash-Kryvets, Valery
Barkovich, Oxana
On the Tits alternative for some generalized triangle groups
topic_facet Tits alternative
generalized triangle group
free subgroup
20E06
20E07
20H10
format Article
author Beniash-Kryvets, Valery
Barkovich, Oxana
author_facet Beniash-Kryvets, Valery
Barkovich, Oxana
author_sort Beniash-Kryvets, Valery
title On the Tits alternative for some generalized triangle groups
title_short On the Tits alternative for some generalized triangle groups
title_full On the Tits alternative for some generalized triangle groups
title_fullStr On the Tits alternative for some generalized triangle groups
title_full_unstemmed On the Tits alternative for some generalized triangle groups
title_sort on the tits alternative for some generalized triangle groups
description One says that the Tits alternative holds for a finitely generated group \(\Gamma\) if \(\Gamma\) contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized triangle groups \(T(k,l,m,R)=\langle a,b; a^k=b^l=R^m(a,b)=1\rangle\). In the paper Rosenberger's conjecture is proved for groups \(T(2,l,2,R)\) with \(l=6,12,30,60\) and some special groups \(T(3,4,2,R)\).
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/988
work_keys_str_mv AT beniashkryvetsvalery onthetitsalternativeforsomegeneralizedtrianglegroups
AT barkovichoxana onthetitsalternativeforsomegeneralizedtrianglegroups
first_indexed 2025-12-02T15:45:23Z
last_indexed 2025-12-02T15:45:23Z
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