On the Fitting length of \(H_{pq}(G)\)
type: Item
instance of: scholarly article
title: On the Fitting length of \(H_{pq}(G)\)
zbMATH Open document ID: 0674.20008
DOI: 10.1007/BF01190207
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: For a natural number \(n\) the generalized Hughes subgroup \(H_ n(G)\) of a group \(G\) is defined as \(H_ n(G)=\langle g\in G\mid g^ n\neq 1\rangle\). The following result is proved: Theorem I: Let \(G\) be a finite, solvable group, \(p\) and \(q\) two primes and \(n=p\cdot q\). Then the Fitting length of \(H_ n(G)\) is at most 3, if \(H_ n(G)\neq G\). This theorem is obtained as an immediate consequence of Theorem 2: Let \(G\) be a finite, solvable group, \(H\) a proper, normal subgroup of \(G\) such that the order of every element of \(G\setminus H\) divides \(p\cdot q\), where \(p\) and \(q\) are two distinct prime numbers. Then the Fitting length of \(H\) is at most 3. This bound is best possible.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4103331
zbMATH Keywords: generalized Hughes subgroup
zbMATH Keywords: finite solvable groups
zbMATH Keywords: Fitting lengths
author: Gülin Ercan
author: İsmail Ş. Güloğlu
MaRDI profile type: Publication
cites work: On the Fitting length of generalized Hughes subgroup
cites work: The Fitting length of the Hughes subgroup
cites work: Q3934684
cites work: The Fitting length of solvable \(H_{p^ n}\)-groups
full work available at URL: https://doi.org/10.1007/bf01190207
OpenAlex ID: W2041783234
description: scientific article; zbMATH DE number 4103331