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Annihilators of derivations with Engel conditions on lie ideals

Rendiconti del Circolo Matematico di Palermo, 2003
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A condition for an area-preserving mapping to be in the Engel’s form

Journal of Mathematical Physics, 2000
We establish explicit expressions of restrictions on the coefficients of nonlinear terms in a two-dimensional area-preserving polynomial map imposed by the property of area preserving. We also establish a necessary and sufficient condition for a two-dimensional area-preserving generic polynomial map to be in the Engel’s form.
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Engel donditions on groups

1964
Let g,c denote positive integers. A group is said to have type (g→c) if every subgroup which can be generated by g elements is nilpotent of class at most c. A result of R. H. Bruck shows that groups of type (4→5) without elements of order 2 are nilpotent of class at most 7.
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A Generalization of Engel Conditions with Derivations in Rings

Communications in Algebra, 2011
Let R be a prime ring of characteristic different from 2 with Z the center of R and d a nonzero derivation of R. Let k, m, n be fixed positive integers. If ([d(x k ), x k ] n ) m  ∈ Z for all x ∈ R, then R satisfies S 4, the standard identity in 4 variables.
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The nilpotency of Leibniz algebras with Engel condition

Moscow University Mathematics Bulletin, 2011
It is proved that a Leibniz algebra over a field of zero characteristic with the Engel condition is nilpotent.
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Engel Elements in Groups with the Minimal Condition

Journal of the London Mathematical Society, 1973
Martin, J. E., Pamphilon, J. A.
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Engel’s law in China: Some new evidence

Review of Development Economics, 2022
Menggen Chen
exaly  

Disparate changes of living standard in China: perspective from Engel's coefficient

China Agricultural Economic Review, 2023
Fujin Yi, Xu Tian
exaly  

Engel conditions

1974
Ralph K. Amayo, Ian Stewart
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