Degree-problems. I: Squarefree character degrees
type: Item
instance of: scholarly article
title: Degree-problems. I: Squarefree character degrees
zbMATH Open document ID: 0574.20006
DOI: 10.1007/BF01270483
author: Bertram Huppert
author: Olaf Manz
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Let \(G\) be a finite group with the property that all its irreducible complex characters have squarefree degrees. The authors show that in the case of \(G\) being solvable there are universal bounds for the derived length and the nilpotent length of \(G\), which are 4 and 3, respectively; if \(G\) is nonsolvable they show that \(G\) is the direct product of the alternating group \(A_7\) and a solvable group \(N\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3916538
zbMATH Keywords: irreducible complex characters
zbMATH Keywords: squarefree degrees
zbMATH Keywords: derived length
zbMATH Keywords: nilpotent length
MaRDI profile type: Publication
cites work: Q5634146
cites work: The existence of regular orbits for nilpotent groups
cites work: Projective character tables for the finite simple groups of order less than one million
cites work: Q3934684
cites work: Q4103728
cites work: The p-parts of character degrees in p-solvable groups
cites work: Q3952291
cites work: Q5623876
cites work: Endliche nicht-auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind
cites work: The non-abelian simple groups g, |g| < 106— character tables
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description: scientific article; zbMATH DE number 3916538