Free Subgroups in Certain Generalized Triangle Groups of Type (2, m, 2)

被引：0
作者：
James Howie
Gerald Williams
机构：
[1] Heriot-Watt University,School of Mathematical and Computer Sciences
[2] University of Kent,Institute of Mathematics, Statistics and Actuarial Science
来源：
Geometriae Dedicata | 2006年 / 119卷
关键词：
Generalised triangle group; Free subgroup; Tits alternative; 20F05; 20E05; 57M07;
D O I：
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摘要：
A generalized triangle group is a group that can be presented in the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = \langle x,y | x^p = y^q = w(x,y)^{r} = 1 \rangle$$\end{document} where p,q,r ≥ 2 and w(x,y) is a cyclically reduced word of length at least 2 in the free product \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{Z}_{p}*\mathbb{Z}_{q}=\langle x,y x^p = y^q = 1\rangle$$\end{document}. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p,q,r) is one of (3, 3, 2), (3, 4, 2), (3, 5, 2), or (2, m, 2) where m=3, 4, 5, 6, 10, 12, 15 , 20, 30, 60. In this paper, we show that the Tits alternative holds in the cases (p,q,r)=(2, m, 2) where m=6, 10, 12, 15, 20, 30, 60.
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页码：181 / 197
页数：16
相关论文
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