(1,1)-bi-Engel Lie ring

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This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
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VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

Definition

A Lie ring L is termed a (1,1)-bi-Engel Lie ring if it satisfies the following:

[[u,x],[u,y]] = 0 \ \forall \ u,x,y \in L

For more, see bi-Engel Lie ring.

Facts

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
2-bi-Engel Lie ring
Lie ring of nilpotency class two
Lie ring of nilpotency class three
Metabelian Lie ring
3-locally metabelian Lie ring