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# Homology, Homotopy and Applications

## Volume 9 (2007)

### Number 2

### On higher nil groups of group rings

Pages: 95 – 100

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n2.a3

#### Author

#### 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 $i\geq 2, j\geq i-1$.

#### Keywords

$K$-theory; nil groups

#### 2010 Mathematics Subject Classification

19A31, 19C99, 19D35