Splitting automorphisms of prime order.
type: Item
instance of: scholarly article
title: Splitting automorphisms of prime order.
zbMATH Open document ID: 1053.20022
DOI: 10.1007/BF02871930
author: Enrico Jabara
publication date: 2004-09-07T00:00:00Z
review text: Let \(G\) be a finite group, and \(\sigma\) an automorphism of \(G\) of order \(p\) (an odd prime). If for all \(g\in G\) one has \(gg^\sigma\cdots g^{\sigma^{pd-1}}=1\) with \((6p,d)=1\), then \(G\) is solvable. The paper continues and uses several well-known studies on generalized f.p.f. automorphisms of a group.
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 2099234
zbMATH Keywords: fixed point free automorphisms
zbMATH Keywords: splitting automorphisms
zbMATH Keywords: solvability of finite groups
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
cites work: Die Nilpotenz der \(H_ p\)-Gruppen
cites work: Eine Verallgemeinerung von fixpunktfreien Automorphismen endlicher Gruppen
full work available at URL: https://doi.org/10.1007/bf02871930
OpenAlex ID: W2089931798
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 2099234