Generalised triangle groups of type \((3,q,2)\)

• Date: 2018
• Main Author: Howie, James
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Generalized triangle groups; Tits alternative; 20F05; 20F06; 20E05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/730
• Journal Title: Algebra and Discrete Mathematics

If \(G\) is a group with a presentation of the form \(\langle x,y|x^3=y^q=W(x,y)^2=1\rangle\), then either \(G\) is virtually soluble or \(G\) contains a free subgroup of rank \(2\). This provides additional evidence in favour of a conjecture of Rosenberger.