Units in group rings of free products of prime cyclic groups

http://dx.doi.org/10.4153/CJM-1998-016-2
Canad. J. Math. 50(1998), 312-322

  Published:1998-04-01
 Printed: Apr 1998

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