Finite solvable groups with at most two nonlinear irreducible characters of each degree.
type: Item
instance of: scholarly article
title: Finite solvable groups with at most two nonlinear irreducible characters of each degree.
zbMATH Open document ID: 1162.20007
author: Guohua Qian
author: Yanming Wang
author: Huaquan Wei
published in: Journal of Algebra
publication date: 2008-12-05T00:00:00Z
review text: In earlier work, \textit{Y. Berkovich} has characterized the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity 1 [J. Algebra 184, No. 2, 584-603 (1996; Zbl 0861.20008)], and \textit{Y. Berkovich, D. Chillag} and \textit{M. Herzog} have described in detail the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity 1 except for possibly one which has multiplicity 2 [Proc. Am. Math. Soc. 115, No. 4, 955-959 (1992; Zbl 0822.20004)]. In the paper under review the authors use these results to give a detailed description of the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity not exceeding 2. The list is too long to be stated here in detail, and the proof is quite technical.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5378361
zbMATH Keywords: finite solvable groups
zbMATH Keywords: multiplicities of character degrees
zbMATH Keywords: nonlinear irreducible characters
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.07.016
OpenAlex ID: W2079794125
cites work: Finite solvable groups in which only two nonlinear irreducible characters have equal degrees
cites work: Finite Groups in which the Degrees of the Nonlinear Irreducible Characters are Distinct
cites work: Finite nonsolvable groups in which only two nonlinear irreducible characters have equal degrees
cites work: Finite groups with almost distinct character degrees.
cites work: Suzuki 2-groups
cites work: Endliche Gruppen I
cites work: Q4103728
cites work: Complex group algebras of finite groups: Brauer’s Problem 1
cites work: Conjugacy Classes Outside a Normal Subgroup
cites work: Q4673095
cites work: Fitting heights of solvable groups with few character degrees
DOI: 10.1016/J.JALGEBRA.2008.07.016
description: scientific article; zbMATH DE number 5378361