The q-parts of degrees of Brauer characters of solvable groups
type: Item
instance of: scholarly article
title: The q-parts of degrees of Brauer characters of solvable groups
zbMATH Open document ID: 0681.20007
author: Olaf Manz
author: Thomas Wolf
published in: Illinois Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let G be a finite solvable group, and let p and q be different primes. The authors show that, if \(q^{e+1}\) does not divide the degree of any irreducible Brauer character of G in characteristic p then the derived length of a Sylow p-subgroup of G is at most \(4e+3\). Similarly, if \(p^{e+1}\) does not divide the degree of any irreducible Brauer character of G in characteristic p then the p-rank of \(G/O_ p(G)\) is at most pe/(p-1); here the p-rank of a finite solvable group H is the largest integer r such that \(p^ r\) is the order of a p-chief factor of H. Some consequences and related results are also proved.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4114863
zbMATH Keywords: finite solvable group
zbMATH Keywords: degree
zbMATH Keywords: irreducible Brauer character
zbMATH Keywords: derived length
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: p-rank
zbMATH Keywords: p-chief factor
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4114863