Rationality and normal 2-complements.
type: Item
instance of: scholarly article
title: Rationality and normal 2-complements.
zbMATH Open document ID: 1159.20009
author: Gabriel Navarro
author: Lucia Sanus
published in: Journal of Algebra
publication date: 2008-11-12T00:00:00Z
review text: Let \(G\) be a finite group, and denote by \(\text{Irr}_\mathbb{Q}(G)\) the set of rational valued irreducible characters of \(G\). The following results are proved: (i) Let \(P\) be a Sylow 2-subgroup of \(G\). Then all characters in \(\text{Irr}_\mathbb{Q}(G)\) are linear if and only if \(G\) has a normal 2-complement, every rational element of \(G\) is a 2-element and all characters in \(\text{Irr}_\mathbb{Q}(P)\) are linear. (ii) If all rational 2-elements of \(G\) are central in \(G\), then \(G\) has a normal 2-complement. The authors remark that the proof of the first result depends on CFSG, whereas the proof of the second only uses ordinary character theory.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 5365174
zbMATH Keywords: finite groups
zbMATH Keywords: rational characters
zbMATH Keywords: rational classes
zbMATH Keywords: normal complements
zbMATH Keywords: linear characters
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.02.036
OpenAlex ID: W2019631609
cites work: Nearly odd-order and nearly real finite groups
cites work: A characterization of groups in terms of the degrees of their characters. II
cites work: Q4312077
cites work: Rational irreducible characters and rational conjugacy classes in finite groups
DOI: 10.1016/J.JALGEBRA.2008.02.036
description: scientific article; zbMATH DE number 5365174