Finite groups whose irreducible Brauer characters have prime power degrees.
type: Item
instance of: scholarly article
title: Finite groups whose irreducible Brauer characters have prime power degrees.
zbMATH Open document ID: 1310.20015
author: H. P. Tong-Viet
published in: Israel Journal of Mathematics
publication date: 2014-10-24T00:00:00Z
review text: Let \(p\) be a prime. The author classifies the finite quasisimple groups all of whose irreducible \(p\)-Brauer characters have prime power degrees. As a corollary, for \(p\neq 2\), the author obtains a classification of the finite nonsolvable groups all of whose irreducible \(p\)-Brauer characters have prime power degrees. Another consequence is the classification, for an arbitrary prime \(p\), of all finite groups whose nonlinear irreducible \(p\)-Brauer characters have prime degrees.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 6361336
zbMATH Keywords: finite quasisimple groups
zbMATH Keywords: irreducible Brauer characters
zbMATH Keywords: character degrees
zbMATH Keywords: prime graphs
zbMATH Keywords: defect zero graphs
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: s11856-014-1086-z
OpenAlex ID: W1964650366
cites work: On \(p\)-blocks of symmetric and alternating groups with all irreducible Brauer characters of prime power degree.
cites work: Prime divisors of irreducible character degrees and of conjugacy class sizes in finite groups
cites work: Primes dividing the degrees of the real characters.
cites work: Defect zero blocks for finite simple groups
cites work: A reduction theorem for the Alperin weight conjecture.
cites work: Subgroups of prime power index in a simple group
cites work: Low-dimensional representations of quasi-simple groups
cites work: ON THE LOCAL CONTROL OF SCHUR MULTIPLIERS
cites work: Solvable groups, all of whose irreducible representations in characteristic p have prime degrees
cites work: Q4012093
cites work: Q3413656
cites work: A characterization of groups in terms of the degrees of their characters
cites work: A characterization of groups in terms of the degrees of their characters. II
cites work: The Minimal Degrees of Faithful Representations of the Sporadic Simple Groups and their Covering Groups
cites work: Solvable groups with \(p\)-modular character degrees of prime power
cites work: Connectedness of degree graphs of nonsolvable groups.
cites work: Small Degree Representations of Finite Chevalley Groups in Defining Characteristic
cites work: Zeros of Brauer characters and the defect zero graph
cites work: Prime power degree representations of quasi-simple groups
cites work: Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind. (Finite solvable groups all whose character degrees are prime powers)
cites work: Endliche nicht-auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind
cites work: On the Number of Components of a Graph Related to Character Degrees
cites work: A finite simple group of Lie type has p-blocks with different defects, \(p\neq 2\)
cites work: Q4387775
cites work: Brauer Characters of Prime Power Degrees and Conjugacy Classes of Prime Power Lengths
DOI: 10.1007/S11856-014-1086-Z
description: scientific article; zbMATH DE number 6361336