Induction and computation of Bass Nil Groups for finite groups
Ian Hambleton, Wolfgang Lueck

TL;DR
This paper investigates the structure of Bass Nil-groups for finite groups, showing they can be generated from p-subgroups via induction, twisting, and Verschiebung maps, with improved torsion estimates for $NK_0(ZG)$.
Contribution
It introduces a new method to generate Bass Nil-groups from elementary subgroups using induction and specific homomorphisms, improving understanding of their structure.
Findings
Bass Nil-groups are generated from p-subgroups by induction and twisting maps.
The structure of $NK_n(RG)$ can be understood via elementary subgroups.
An improved estimate of the torsion exponent for $NK_0(ZG)$ is provided.
Abstract
Let G be a finite group. We show that the Bass Nil-groups , , 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 are generated by induction from elementary subgroups. For we get an improved estimate of the torsion exponent.
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