McKay natural correspondences on characters

Navarro, Gabriel; Tiep, Pham Huu; Vallejo, Carolina

doi:10.2140/ant.2014.8.1839

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McKay natural correspondences on characters

Gabriel Navarro, Pham Huu Tiep and Carolina Vallejo

Vol. 8 (2014), No. 8, 1839–1856

DOI: 10.2140/ant.2014.8.1839

Abstract

Let $G$ be a finite group, let $p$ be an odd prime, and let $P \in {Syl}_{p} (G)$ . If $N_{G} (P) = P C_{G} (P)$ , 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

Vol. 8, No. 8, 2014