Induction and computation of Bass Nil Groups for finite groups

Let G be a finite group. We show that the Bass Nil-groups $NK_n(RG)$, $n \in Z$, are generated from the p-subgroups of G by induction maps, certain twisting maps depending on elements in the centralizers of the p-subgroups, and the Verschiebung homomorphisms. As a consequence, the groups $NK_n(RG)$ are generated by induction from elementary subgroups. For $NK_0(ZG)$ we get an improved estimate of the torsion exponent.

💡 Research Summary

The paper addresses the long‑standing problem of describing the structure of Bass Nil‑groups $NK_n(RG)$ for a finite group $G$ and a coefficient ring $R$. These groups arise as the “nil‑part” of the algebraic $K$‑theory of the group ring $RG$, namely the kernel of the canonical map $K_n(RG