On the Fitting length of generalized Hughes subgroup
type: Item
instance of: scholarly article
title: On the Fitting length of generalized Hughes subgroup
zbMATH Open document ID: 0674.20007
DOI: 10.1007/BF01199108
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: In the search of reasonable generalizations of a result of \textit{A. Espuelas} [J. Algebra 105, 365-371 (1987; Zbl 0604.20021)] the following result is obtained. Theorem: Let H be a finite, solvable group admitting an automorphism \(\alpha\) of prime order p. Suppose that \([H,\alpha]=H\) and let \(G=H<\alpha >\) be the semidirect product of H and \(<\alpha >\). If the order of every element in \(G\setminus H\) divides p.q where q is a prime different from p, then the Fitting length of H is at most 2.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 4103330
zbMATH Keywords: Hughes subgroup
zbMATH Keywords: finite solvable group
zbMATH Keywords: automorphism of prime order
zbMATH Keywords: Fitting length
author: Gülin Ercan
author: İsmail Ş. Güloğlu
MaRDI profile type: Publication
cites work: Automorphism of prime order of solvable groups whose subgroups of fixed points are nilpotent
cites work: The Fitting length of the Hughes subgroup
cites work: Solvable groups admitting an ''almost fixed point free'' automorphism of prime order
cites work: The \(H_p\)-problem and the structure of \(H_p\)-groups
cites work: Q3934684
cites work: Die Nilpotenz der \(H_ p\)-Gruppen
cites work: The Fitting length of solvable \(H_{p^ n}\)-groups
full work available at URL: https://doi.org/10.1007/bf01199108
OpenAlex ID: W2093398064
description: scientific article; zbMATH DE number 4103330