Infinite locally soluble \(k\)-Engel groups
type: Item
instance of: scholarly article
title: Infinite locally soluble \(k\)-Engel groups
zbMATH Open document ID: 0791.20038
author: Lucia Serena Spiezia
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1993-02-18T00:00:00Z
full work available at URL: https://eudml.org/doc/244332
review text: Summary: We deal with the class \({\mathcal E}^*_ k\) of groups \(G\) for which whenever we choose two infinite subsets \(X\), \(Y\) there exist two elements \(x \in X\), \(y \in Y\) such that \([x,\underbrace{y,\dots,y}_ k]= 1\). We prove that an infinite finitely generated soluble group in the class \({\mathcal E}^*_ k\) is in the class \({\mathcal E}_ k\) of \(k\)-Engel groups. Furthermore, with \(k = 2\), we show that if \(G \in {\mathcal E}^*_ 2\) is an infinite locally soluble or hyperabelian group then \(G \in {\mathcal E}_ 2\).
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 124184
zbMATH Keywords: infinite subsets
zbMATH Keywords: finitely generated soluble group
zbMATH Keywords: \(k\)-Engel groups
zbMATH Keywords: infinite locally soluble
zbMATH Keywords: hyperabelian group
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 124184