On a problem of P. Hall for Engel words.
type: Item
instance of: scholarly article
title: On a problem of P. Hall for Engel words.
zbMATH Open document ID: 1236.20044
author: Alireza Abdollahi
author: Francesco Russo
published in: Archiv der Mathematik
publication date: 2011-12-14T00:00:00Z
review text: Let \([x,y]=[x,{_1y}]\) and \([[x,{_ky}],y]=[x,{_{k+1}y}]\). In this article the word \(e_n(x,y)=[x,{_ny}]\) and the corresponding set \(\{E_n\}(G)\) of words, the word subgroups \(E_n(G)\) and the marginal subgroups \(E^*(G)\) are considered. Results: If \(\{E_2\} (G)\) is finite, then \(E_2(G)\) is finite; further \(G/E_2^*(G)\) is finite if \(G\) is finitely generated (Theorem 2.3). -- If \(k\in\{3,4\}\) and \(\{E_k\}(G)\) is finite, then \(E_k(G)\) is finite (Theorem 2.4). Inequalities on the order and the number of generators of \(G/E_2^*(G)\) are given.
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F12
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 5988200
zbMATH Keywords: Engel words
zbMATH Keywords: marginal subgroups
zbMATH Keywords: finiteness conditions
zbMATH Keywords: numbers of generators
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: s00013-011-0312-8
OpenAlex ID: W2138907334
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DOI: 10.1007/S00013-011-0312-8
description: scientific article; zbMATH DE number 5988200