The Tits alternative for generalized triangle groups of type \((3,4,2)\)

• Date: 2018
• Main Authors: Howie, James, Williams, Gerald
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Generalized triangle group; Tits alternative; free subgroup; 20F05; 20E05; 57M07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/826
• Journal Title: Algebra and Discrete Mathematics

A generalized triangle group is a group that can be presented in the form \( G = \langle {x,y}\ |{x^p=y^q=w(x,y)^r=1} \rangle \) where \(p,q,r\geq 2\) and \(w(x,y)\) is a cyclically reduced word of length at least \(2\) in the free product \(\mathbb{Z}_p*\mathbb{Z}_q= \langle {x,y}\ |{x^p=y^q=1}\ran...