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

Let G be a finite group and let p be a prime. We show that the unit group of the integral group ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \mathbb{Z}[G] $$ \end{document} contains the free product Zp * Z if and only if G has a noncentral element of order p. Moreover, when this occurs, then the Zp-part of the free product can be taken to be a suitable noncentral subgroup of G of order p.