On the Engel problem
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 53-62

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It is shown that a variety of Lie algebras over a field of characteristic zero satisfying an Engel condition of bounded index and for which the growth of the codimensions of the verbal ideal is at most exponential is nilpotent. Bibliography: 8 titles.
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S. P. Mishchenko. On the Engel problem. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a3/