Let G be a free product of cyclic groups of prime order. The structure
of the unit group U(QG) of the rational group ring QG is given in ter
ms of free products and amalgamated free products of groups. As an app
lication, all finite subgroups of U(QG), up to conjugacy, are describe
d and the Zassenhaus Conjecture for finite subgroups in ZG is proved.
A strong version of the Tits Alternative for U(QG) is obtained as a co
rollary of the structural result.