. On Rosenberger's conjecture for generalized triangle groups of types (2,10,2) and (2,20,2)

Abstract

Tits proved that if G is a finitely generated linear group then G contains either a non abelian free subgroup or a solvable subgroup of finite index. Let G be an arbitrary finitely generated group. One says that the Tits alternative holds for G if G contains either a non abelian free subgroup or a solvable subgroup of finite index. In this paper we prove the following theorem. Let G be a generalized triangle group of the type (2,10,2) or (2,20,2). Then G contains a free subgroup of rank 2. Hence the Tits alternative holds for G.