Some character degree conditions implying solvability of finite groups.
type: Item
instance of: scholarly article
title: Some character degree conditions implying solvability of finite groups.
zbMATH Open document ID: 1277.20009
author: Kamal Aziziheris
published in: Algebras and Representation Theory
publication date: 2013-06-13T00:00:00Z
review text: Continuing in the spirit of some of his earlier work, the author proves that if \(G\) is a finite group whose character degree set is a subset of \(\{1,a,b,c,ab,ac\}\) for some pairwise relatively coprime integers \(a\), \(b\), and \(c\), then \(G\) is solvable, or \(\{a,b,c\}=\{2^f-1,2^f,2^f+1\}\) for some \(f\geq 2\) and \(\{1,a,b,c\}\) is the set of character degrees of \(G\).
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 6175484
zbMATH Keywords: finite groups
zbMATH Keywords: character degree sets
zbMATH Keywords: solvability
zbMATH Keywords: solvable groups
zbMATH Keywords: character degrees
zbMATH Keywords: almost simple groups
zbMATH Keywords: irreducible complex characters
MaRDI profile type: Publication
full work available at URL: s10468-011-9328-9
OpenAlex ID: W2058139655
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DOI: 10.1007/S10468-011-9328-9
description: scientific article; zbMATH DE number 6175484