Geodesic
The nilpotency class of the~sandwich subalgebra of simple finite-dimensional Lie algebras
Sbornik. Mathematics, Tome 186 (1995) no. 8, pp. 1173-1184

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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 $p=5$). 
@article{SM_1995_186_8_a3,
     author = {S. A. Kirillov},
     title = {The nilpotency class of the~sandwich subalgebra of simple finite-dimensional {Lie} algebras},
     journal = {Sbornik. Mathematics},
     pages = {1173--1184},
     publisher = {mathdoc},
     volume = {186},
     number = {8},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_8_a3/}
}
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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/