On the Tits alternative for some generalized triangle groups

Abstract

One says that the Tits alternative holds for a finitely generated group \(\Gamma\) if \(\Gamma\) contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized triangle groups \(T(k,l,m,R)=\langle a,b; a^k=b^l=R^m(a,b)=1\rangle\). In the paper Rosenberger's conjecture is proved for groups \(T(2,l,2,R)\) with \(l=6,12,30,60\) and some special groups \(T(3,4,2,R)\).