On linear relations between character values
type: Item
instance of: scholarly article
title: On linear relations between character values
zbMATH Open document ID: 0358.20006
DOI: 10.1016/0021-8693(77)90216-2
author: Marcel Herzog
published in: Journal of Algebra
publication date: 1977-01-01T00:00:00Z
review text: Finite groups \(G\) satisfying the following properties are characterized: There exist non-conjugate elements \(s\) and \(u\) of \(G\) and complex numbers \(a\), \(b\) and \(c\), \(ab \neq 0\), such that \(aX(s) +bX(u) = c\) is satisfied: (i) by every irreducible character of \(G\), or (ii) by every non-principal irreducible character of \(G\), but not by the principal character. In case (i), \(G\) turns out to be a solvable group of derived length at most 3. In case (ii) it is shown that if \(|G| > 3\), then either \(G\) is a Frobenius group of order \(2n\), \(n\) odd, with the kernel of order \(n\), or \(G \cong \text{PSL}(2,2^n)\), \(n \geq 2\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D99
zbMATH DE Number: 3558044
MaRDI profile type: Publication
full work available at URL: 0021-8693(77)90216-2
OpenAlex ID: W2080727969
cites work: Q5551256
cites work: Q5577154
cites work: On groups with extremal blocks
cites work: Endliche Gruppen I
cites work: A characterization of groups in terms of the degrees of their characters
cites work: A characterization of groups in terms of the degrees of their characters. II
description: scientific article; zbMATH DE number 3558044