(1,1)-bi-Engel Lie ring
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 is termed a (1,1)-bi-Engel Lie ring if it satisfies the following:
![{\displaystyle [[u,x],[u,y]]=0\ \forall \ u,x,y\in L}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e4edff6f1df2e64991812ef5cc1c1f4318582a)
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 |