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 investigates the Bass Nil‑groups (NK_n(RG)) for a finite group (G) and an arbitrary unital ring (R). These groups are defined as the kernel of the evaluation map (K_n(RG