Embedding free products in the unit group of an integral group ring

Abstract.

Let G be a finite group and let p be a prime. We show that the unit group of the integral group ring $\mathbb{Z}[G]$ contains the free product Z _p * Z if and only if G has a noncentral element of order p. Moreover, when this occurs, then the Z _p -part of the free product can be taken to be a suitable noncentral subgroup of G of order p.