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Algebra and Discrete Mathematics, 2008, Issue 4, Pages 40–48 (Mi adm177)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

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

James Howiea, Gerald Williamsb

a Maxwell Institute of Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
b Department of Mathematical Sciences, University of Essex, Colchester, CO4 3SQ United Kingdom
Full-text PDF (222 kB) Citations (1)
Abstract: 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 $\mathbb Z_p*\mathbb Z_q=\langle{x,y}{x^p=y^q=1}\rangle$. 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 $(2,3,2)$, $(2,4,2)$, $(2,5,2)$, $(3,3,2)$, $(3,4,2)$ or $(3,5,2)$. Building on a result of Benyash–Krivets and Barkovich from this journal, we show that the Tits alternative holds in the case $(p,q,r)=(3,4,2)$.
Keywords: Generalized triangle group, Tits alternative, free subgroup.
Received: 15.05.2007
Revised: 16.10.2007
Bibliographic databases:
Document Type: Article
MSC: 20F05, 20E05, 57M07
Language: English
Citation: James Howie, Gerald Williams, “The Tits alternative for generalized triangle groups of type $(3,4,2)$”, Algebra Discrete Math., 2008, no. 4, 40–48
Citation in format AMSBIB
\Bibitem{HowWil08}
\by James~Howie, Gerald~Williams
\paper The Tits alternative for generalized triangle groups of type~$(3,4,2)$
\jour Algebra Discrete Math.
\yr 2008
\issue 4
\pages 40--48
\mathnet{http://mi.mathnet.ru/adm177}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2541170}
\zmath{https://zbmath.org/?q=an:1178.20030}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Algebra and Discrete Mathematics
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