Groups with few characters of small degrees
type: Item
instance of: scholarly article
title: Groups with few characters of small degrees
zbMATH Open document ID: 0958.20008
DOI: 10.1007/BF02808187
published in: Israel Journal of Mathematics
publication date: 2001-04-17T00:00:00Z
review text: Let \(\sigma_d(G)\) be the sum of squares of degrees of all those irreducible complex characters whose degrees are not divisible by \(d\); here \(d>1\) divides the order of the finite group \(G\). We have that \(d\) divides \(\sigma_d(G)\). The case where equality occurs, leads to a Frobenius group \(G\) whose kernel has index \(d\) in \(G\). In this paper the case \(\sigma_d(G)=2d\) is studied in some detail; in particular if \(G\) is a 2-group, then it happens to be of maximal class.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 1310644
zbMATH Keywords: character degrees
zbMATH Keywords: \(2\)-groups of maximal class
zbMATH Keywords: irreducible complex characters
zbMATH Keywords: finite groups
zbMATH Keywords: Frobenius groups
author: Yakov Berkovich
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
cites work: Degrees of Irreducible Characters and Normal p-Complements
cites work: Finite groups with small sums of degrees of some nonlinear irreducible characters
cites work: Q4375272
cites work: Endliche Gruppen I
cites work: Q4103728
cites work: Q4004216
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description: scientific article; zbMATH DE number 1310644