Vol. 8, No. 8, 2014

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McKay natural correspondences on characters

Gabriel Navarro, Pham Huu Tiep and Carolina Vallejo

Vol. 8 (2014), No. 8, 1839–1856
Abstract

Let G be a finite group, let p be an odd prime, and let P Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.

Keywords
McKay conjecture, self-normalizing Sylow subgroup, $p$-decomposable Sylow normalizer
Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 20C20
Milestones
Received: 31 January 2014
Revised: 17 June 2014
Accepted: 25 August 2014
Published: 28 November 2014
Authors
Gabriel Navarro
Departamento de Álgebra
Universitat de València
Doctor Moliner, 50
46100 Burjassot
València
Spain
Pham Huu Tiep
Department of Mathematics
University of Arizona
617 North Santa Rita Avenue
Tucson, AZ 85721
United States
Carolina Vallejo
Departamento de Álgebra
Universitat de València
Doctor Moliner, 50
46100 Burjassot
València
Spain