On the image of the trivial source ring in the ring of virtual characters of a finite group

TL;DR

This paper investigates the structure of the cokernel of a canonical homomorphism from the trivial source ring to the ring of p-rational complex characters of a finite group, utilizing advanced biset functor theories.

Contribution

It applies Boltje and Co extcyrillicsken's fibered biset functor theory and Bouc's rational p-biset functors to explicitly determine the cokernel's structure.

Findings

Identifies the cokernel structure of the homomorphism

Utilizes fibered biset functor theory for analysis

Provides new insights into the relationship between trivial source rings and p-rational characters

Abstract

We examine the cokernel of the canonical homomorphism from the trivial source ring of a finite group to the ring of $p$-rational complex characters. We use Boltje and Co\c{s}kun's theory of fibered biset functors to determine the structure of the cokernel. An essential tool in the determination of this structure is Bouc's theory of rational $p$-biset functors.