Cohn localization of finite group rings

TL;DR

This paper provides a comprehensive description of the Cohn localization of the group ring Z[G] at the augmentation map for any finite group G, advancing understanding in algebraic localization.

Contribution

It offers a complete characterization of the Cohn localization for finite group rings, filling a gap in algebraic localization theory.

Findings

Explicit description of the Cohn localization for all finite groups

Extension of known results to broader classes of finite groups

Enhanced understanding of algebraic structures in group rings

Abstract

The purpose of this paper is to give a complete description of the Cohn localization of the augmentation map $Z[G]\rightarrow Z$ when $G$ is any finite group.