Solvable groups having only three rational classes of 2-elements.
type: Item
instance of: scholarly article
title: Solvable groups having only three rational classes of 2-elements.
zbMATH Open document ID: 1233.20017
author: I. M. Isaacs
author: Gabriel Navarro
published in: Archiv der Mathematik
publication date: 2011-10-25T00:00:00Z
review text: A result by \textit{A. Moretó} and \textit{G. Navarro} [Isr. J. Math. 163, 85-92 (2008; Zbl 1152.20011)] implies that if the number of real conjugacy classes of a finite group \(G\) is at most three, then \(G\) is solvable with 2-length at most 1. The paper under review shows that under the additional hypothesis that \(G\) is solvable, the conclusion remains true under the much weaker hypothesis that \(G\) has at most three rational conjugacy classes.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5963412
zbMATH Keywords: rational classes
zbMATH Keywords: real characters
zbMATH Keywords: 2-lengths
zbMATH Keywords: numbers of real conjugacy classes
zbMATH Keywords: finite solvable groups
zbMATH Keywords: rational conjugacy classes
MaRDI profile type: Publication
full work available at URL: s00013-011-0303-9
OpenAlex ID: W2067952645
cites work: Real‐Valued Characters of Solvable Groups
cites work: Q3934684
cites work: Characters of \(\pi\)-separable groups
cites work: Normal \(p\)-complements and fixed elements.
cites work: Groups with three real valued irreducible characters.
cites work: 2-length and rational characters of odd degree.
DOI: 10.1007/S00013-011-0303-9
description: scientific article; zbMATH DE number 5963412