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Israel Journal of Mathematics, 2003
A group is called Engel if every two elements \(a,b\) of the group satisfy a relation of the form \[ [\cdots[[a,b],b],\dots,b]=1, \] where \([a,b]=a^{-1}b^{-1}ab\). In 1992, \textit{J. S. Wilson} and \textit{E. I. Zelmanov} [J. Pure Appl. Algebra 81, No. 1, 103-109 (1992; Zbl 0851.17007)] proved that a profinite Engel group is locally nilpotent.
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A group is called Engel if every two elements \(a,b\) of the group satisfy a relation of the form \[ [\cdots[[a,b],b],\dots,b]=1, \] where \([a,b]=a^{-1}b^{-1}ab\). In 1992, \textit{J. S. Wilson} and \textit{E. I. Zelmanov} [J. Pure Appl. Algebra 81, No. 1, 103-109 (1992; Zbl 0851.17007)] proved that a profinite Engel group is locally nilpotent.
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The Quarterly Journal of Mathematics, 1993
The author provides detailed information for the nilpotency class of Lie algebras (over a field \(k\)) satisfying the Engel condition \((\operatorname {ad}b)^n= 0\) for all \(b\), \(n=3,4\). The author shows that for \(n=3\), \(\operatorname {char}k\neq 2,5\), the nilpotency class is \(\leq 4\) (which is the best possible result) and for \(n=4 ...
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The author provides detailed information for the nilpotency class of Lie algebras (over a field \(k\)) satisfying the Engel condition \((\operatorname {ad}b)^n= 0\) for all \(b\), \(n=3,4\). The author shows that for \(n=3\), \(\operatorname {char}k\neq 2,5\), the nilpotency class is \(\leq 4\) (which is the best possible result) and for \(n=4 ...
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The Contribution of Marx and Engels
1992It is at first sight odd to include in a work on feminist political theory a section on classic Marxism, because Karl Marx was not a feminist. This does not mean that he was hostile to female liberation but simply that, unlike Mill or Thompson, he did not see issues of sexual oppression as interesting or important in their own right, and he never made ...
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Once Again on the Alleged Differences Between Engels and Marx
International Critical Thought, 2020Stavros Mavroudeas
exaly