Units and Augmentation Powers in Integral Group Rings

The augmentation powers in an integral group ring $\mathbb{Z}G$ induce a natural filtration of the unit group of $\mathbb{Z}G$ analogous to the filtration of the group $G$ given by its dimension series ${D_n(G)}_{n\ge 1}$. The purpose of the present article is to investigate this filtration, in particular, the triviality of its intersection.