Normal \(p\)-complements and fixed elements.
type: Item
instance of: scholarly article
title: Normal \(p\)-complements and fixed elements.
zbMATH Open document ID: 1206.20022
author: I. M. Isaacs
author: Gabriel Navarro
published in: Archiv der Mathematik
publication date: 2010-10-08T00:00:00Z
review text: It is well-known that if \(K\) is a group of odd order acting on a 2-group \(P\) such that \(K\) fixes all elements of order 2 and 4 in \(P\), then \(K\) acts trivially on \(P\). Recently \textit{G. Navarro} and \textit{L. Sanus} [J. Algebra 320, No. 6, 2451-2454 (2008; Zbl 1159.20009)] proved, using character theory, that \(K\) acts trivially on \(P\) if it fixes all rational elements of \(P\). Noting that elements of order 2 are rational and elements of order 4 are rational if and only if they are real, the authors prove, again using character theory, the following ``intersection'' of these results: \(K\) acts trivially on \(P\) if it fixes all elements of order 2 and all real elements of order 4 in \(P\).
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 5797318
zbMATH Keywords: finite groups
zbMATH Keywords: fixed points
zbMATH Keywords: real elements
zbMATH Keywords: rational elements
zbMATH Keywords: normal complements
MaRDI profile type: Publication
full work available at URL: s00013-010-0162-9
OpenAlex ID: W1983282925
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DOI: 10.1007/S00013-010-0162-9
description: scientific article; zbMATH DE number 5797318