Hypercentral units in integral group rings

Abstract:

In this note, we show that when $G$ is a torsion group the second center of the group of units $U({\mathbb Z}G)$ of the integral group ring ${\mathbb Z}G$ is generated by its torsion subgroup and by the center of $U({\mathbb Z}G)$. This extends a result of Arora and Passi (1993) from finite groups to torsion groups, and completes the characterization of hypercentral units in ${\mathbb Z}G$ when $G$ is a torsion group.