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RESEARCH ARTICLE

Generalised triangle groups of type $\mathbf{(3,q,2)}$

J. Howie

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

Abstract: 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.

Keywords: Generalized triangle groups, Tits alternative.

MSC: 20F05, 20F06, 20E05

Received: 03.05.2012
Revised: 20.06.2012

Language: English

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