Vol. 315, No. 2, 2021

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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
Authors
John Revere McHugh
University of California, Santa Cruz
Santa Cruz, CA
United States