Geodesic
The nilpotency class of the sandwich subalgebra of simple finite-dimensional Lie algebras
Sbornik. Mathematics, Tome 186 (1995) no. 8, pp. 1173-1184 
S. A. Kirillov. The nilpotency class of the sandwich subalgebra of simple finite-dimensional Lie algebras. Sbornik. Mathematics, Tome 186 (1995) no. 8, pp. 1173-1184. http://geodesic.mathdoc.fr/item/SM_1995_186_8_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is shown that the nilpotency class of sandwich subalgebras in Lie algebras of Cartan type and in Melikyan algebras over a field of characteristic $p\geqslant 5$ is equal to $2m-1$, where $m$ is the sum of the heights of the variables. The only exception is the Zassenhaus algebra (and also the Hamiltonian and contact algebras for $p=5$).

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