Generalised triangle groups Seminar

A generalised triangle group is one given by a presentation of the form < x,y | xp = yq = W(x,y)r = 1 > for some word W and integers p,q,r > 1. A long-standing conjecture of Rosenberger says that such groups satisfy a form of Tits alternative - either the group is virtually soluble, or it contains a rank-2 free subgroup. I will give a survey of this problem and sketch some recent results.