Geodesic
The Engel identity and its application
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 419-426 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the case of characteristic zero, the Engel identity implies nilpotence in the variety generated by simple infinite-dimensional Lie algebras of Cartan type. An analogous result is also true for 2-metabelian Lie algebras (an algebra is called 2-metabelian if every 2-generator subalgebra is metabelian) over a field whose characteristic does not divide $5!\,$, which in this case permits one to prove solvability of the variety of 2-metabelian Lie algebras. Bibliography: 10 titles. 
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S. P. Mishchenko. The Engel identity and its application. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 419-426. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a8/

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