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


Daniel Juan-Pineda (Instituto de Matemáticas, Unidad Morelia, Universidad Nacional Autónoma de México, Morelia, Michoacán, Mexico)


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


$K$-theory; nil groups

2010 Mathematics Subject Classification

19A31, 19C99, 19D35

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