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

John Revere McHugh

Vol. 315 (2021), No. 2, 449–476

DOI: 10.2140/pjm.2021.315.449

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 Coşkun’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.

Keywords

trivial source ring, finite groups, biset functors, fibered biset functors, Schur index

Mathematical Subject Classification

Primary: 19A22, 20C20

Milestones

Received: 26 February 2021

Revised: 9 September 2021

Accepted: 29 September 2021

Published: 19 January 2022