On the Fitting length of \(H_ n(G)\)
type: Item
instance of: scholarly article
title: On the Fitting length of \(H_ n(G)\)
zbMATH Open document ID: 0819.20019
author: Gülin Ercan
author: İsmail Ş. Güloğlu
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1994-05-31T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108284
review text: The authors prove the following theorem: Let \(H\) be a finite solvable group, \(\alpha\) an automorphism of \(H\) of prime order acting on \(H\) in such a way that \(p^ 2 \nmid N\) for \(N := \text{lcm}\{o(a);\;a\in H\langle \alpha \rangle \setminus H\}\). If \(4 \nmid N\) then the Fitting length of \(H\) is at most \(m + 4\), \(m\) being the number of prime factors of \(N/p\). Applied to the Hughes subgroups \(H_ n(G) = \langle x \in G; x^ n \neq 1\rangle\) of a finite solvable group \(G\) this result implies that their Fitting length is at most \(m + 3\) if \(H_ n(G) \neq G\) and \(n = p_ 1 \cdot \dots \cdot p_ m\) with pairwise distinct primes \(p_ i\).
reviewed by: Gerhard Kowol
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 492572
zbMATH Keywords: finite solvable group
zbMATH Keywords: automorphism
zbMATH Keywords: Fitting length
zbMATH Keywords: Hughes subgroups
MaRDI profile type: Publication
cites work: On the Fitting length of generalized Hughes subgroup
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description: scientific article; zbMATH DE number 492572