Lie rings and the Engel condition
type: Item
instance of: scholarly article
title: Lie rings and the Engel condition
zbMATH Open document ID: 0358.20051
DOI: 10.1016/0021-8693(74)90070-2
author: A. Braun
published in: Journal of Algebra
publication date: 1974-01-01T00:00:00Z
review text: In his work dealing with the restricted Burnside problem, Kostrikin showed that a Lie ring of prime characteristic \(p\) satisfying an \(n\)-th Engel condition, where \(n\leq p\), is locally nilpotent. Theorem 1 in the paper under review is an extension of this result to the case \(n= p+ 1, p\geq 3\). In proving Theorem 1, the author first proves Theorem 2: A Lie ring of characteristic \(p\geq 3\), without center, satisfying the \(p+ 1\) Engel condition and not satisfying the \(n\)-th Engel condition for \(n\leq p\), contains a non-trivial nilpotent ideal.
Mathematics Subject Classification ID: 20F40
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 3558089
Wikidata QID: Q115367666
MaRDI profile type: Publication
full work available at URL: 0021-8693(74)90070-2
OpenAlex ID: W2024930726
cites work: The Burnside problem
cites work: Lie rings satisfying the Engel condition
cites work: Q5817437
description: scientific article; zbMATH DE number 3558089