The 2-length of the Hughes subgroup
type: Item
instance of: scholarly article
title: The 2-length of the Hughes subgroup
zbMATH Open document ID: 0652.20026
DOI: 10.1007/BF02787122
author: Volker Turau
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The (generalized) Hughes subgroup \(H_{p\quad n}(G)\) of a finite group G (p a prime, \(n\geq 1)\) is defined as the subgroup of G generated by all elements x such that \(x^{p\quad n}\neq 1\). It is conjectured that for finite solvable G with \(1\neq H:=H_{p\quad n}(G)\neq G\) the Fitting length of H is bounded by n, generalizing the Kegel-Hughes-Thompson theorem \((n=1)\). For odd primes p, the conjecture was proved by Espuelas improving weaker results by various authors. In the reviewed paper, the author proves that for \(p=2\) at least the 2-length of H is bounded by n.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 4063364
zbMATH Keywords: generalized Hughes subgroup
zbMATH Keywords: Fitting length
zbMATH Keywords: Kegel-Hughes-Thompson
zbMATH Keywords: 2- length
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02787122
OpenAlex ID: W2095248532
description: scientific article; zbMATH DE number 4063364