Algebra & Number Theory

McKay natural correspondences on characters

Gabriel Navarro, Pham Huu Tiep, and Carolina Vallejo

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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.

Article information

Source
Algebra Number Theory, Volume 8, Number 8 (2014), 1839-1856.

Dates
Received: 31 January 2014
Revised: 17 June 2014
Accepted: 25 August 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730285

Digital Object Identifier
doi:10.2140/ant.2014.8.1839

Mathematical Reviews number (MathSciNet)
MR3285617

Zentralblatt MATH identifier
1320.20010

Subjects
Primary: 20C15: Ordinary representations and characters
Secondary: 20C20: Modular representations and characters

Keywords
McKay conjecture self-normalizing Sylow subgroup $p$-decomposable Sylow normalizer

Citation

Navarro, Gabriel; Tiep, Pham Huu; Vallejo, Carolina. McKay natural correspondences on characters. Algebra Number Theory 8 (2014), no. 8, 1839--1856. doi:10.2140/ant.2014.8.1839. https://projecteuclid.org/euclid.ant/1513730285


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