On the Tits alternative for some generalized triangle groups

Abstract

One says that the Tits alternative holds for a finitely generated group G if G 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 $T(k,l,m,R)=<a,b; a^k=b^l=R^m(a,b)=1>$. 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).