Characters of p'-degree in solvable groups
type: Item
instance of: scholarly article
title: Characters of p'-degree in solvable groups
zbMATH Open document ID: 0358.20005
author: Thomas Wolf
published in: Pacific Journal of Mathematics
publication date: 1978-01-01T00:00:00Z
review text: The groups considered are finite and the group characters are defined over the complex numbers. For a group \(G\) and a prime \(p\), we let \(\text{Irr}(G)\) be the set of irreducible characters of \(G\) and let \(I_p(G) = \{\psi \in \text{Irr}(G)|(p, \psi(1)) = 1\}\). The McKay conjecture proposes \(|I_p(G)| =|I_p(N(P))|\) where \(P \in \text{Syl}_p(G)\). Originally, the conjecture was for simple \(G\) and \(p=2\). \textit{I. M. Isaacs} has proven the result when \(|G|\) is odd and \(p\) is any prime. This paper proves the result for solvable \(G\) and any prime \(p\). For solvable \(G\), this is generalized to sets of primes and normalizers of Hall subgroups.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3558043
MaRDI profile type: Publication
full work available at URL: pjm.1978.74.267
OpenAlex ID: W2038054275
DOI: 10.2140/PJM.1978.74.267
description: scientific article; zbMATH DE number 3558043