Solvability of finite groups admitting \(S_ 3\) as a fixed-point-free group of operators
type: Item
instance of: scholarly article
title: Solvability of finite groups admitting \(S_ 3\) as a fixed-point-free group of operators
zbMATH Open document ID: 0605.20022
author: Hiroshi Fukushima
published in: Hokkaido Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: It is an immediate consequence of the famous theorem of Feit and Thompson that a group G which has a group A, isomorphic to the symmetric group of degree 3 acting on it fixed-point-freely so that \((| G|,| A|)=1\), is soluble. The author gives a proof of this result which does not depend on this result. That this is worth achieving is clear from earlier work of \textit{G. Glauberman} [Math. Z. 84, 120-125 (1964; Zbl 0123.026)]. The paper uses the techniques most likely to succeed with skill and inventiveness. He points out that the result has also recently been obtained by B. Dolman in a Ph.D thesis at the University of Adelaide.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 3977246
zbMATH Keywords: group of automorphisms
zbMATH Keywords: fixed-point-free group of automorphisms
zbMATH Keywords: solvability
reviewed by: A. R. Camina
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381518220
OpenAlex ID: W2085099942
DOI: 10.14492/HOKMJ/1381518220
description: scientific article; zbMATH DE number 3977246