Units in Group Rings of Free Products of Prime Cyclic Groups

Let $G$ be a free product of cyclic groups of prime order. The structure of the unit group $U(\mathbb{Q}G)$ of the rational group ring $\mathbb{Q}G$ is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of $U(\mathbb{Q}G)$ , up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in $\mathbb{Z}G$ is proved. A strong version of the Tits Alternative for $U(\mathbb{Q}G)$ is obtained as a corollary of the structural result.