On higher nil groups of group rings

Abstract

Let $G$ be a finite group and $mathbb{Z}[G]$ its integral group ring. We prove that the nil groups $N^j K_2 \mathbb{Z}[G])$ do not vanish for all $j \geq 1$ and for a large class of finite groups. We obtain from this that the iterated nil groups $N^j K_i (\mathbb{Z}[G])$ are also nonzero for all $i \geq 2, j \geq i - 1$