On One-Relator Groups Having Elements of Finite Order

Abstract

Let G be a one-relator group having torsion. It is easy to show that there exists a normal subgroup N which is of finite index and torsion-free. We prove that N is free iff G is the free product of a free group and a finite cyclic group; N is a proper free product iff G is a proper free product of a free group and a one-relator group. In the proof, use is made of the following result: the elements of finite order in G generate a group which is the free product of conjugates of a finite cyclic group.