Groups having three complex irreducible character degrees
type: Item
instance of: scholarly article
title: Groups having three complex irreducible character degrees
zbMATH Open document ID: 0839.20014
author: Thomas Noritzsch
published in: Journal of Algebra
publication date: 1996-06-11T00:00:00Z
review text: A study is made of the possible sets \(\{1,a,b\}\) consisting of exactly three character degrees. A lot of results was already known. For instance, all the corresponding groups are solvable of derived length \(\leq 3\). Here we see that if \((a,b) =1\), only certain subgroups of affine semi-linear groups and cyclic semi-direct extensions of extraspecial \(p\)-groups occur here in essence. Also the corresponding arithmetical conditions on \(a\), \(b\) are given. There are much other results in this paper, with full proofs and arguments. It is a paper suitable for (advanced) students to study.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 794341
zbMATH Keywords: solvable groups
zbMATH Keywords: character degrees
zbMATH Keywords: affine semi-linear groups
zbMATH Keywords: extraspecial \(p\)-groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: jabr.1995.1213
OpenAlex ID: W1994717928
DOI: 10.1006/JABR.1995.1213
description: scientific article; zbMATH DE number 794341