Geodesic
A solvability criterion for a finite-dimensional Lie algebra
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 5-8

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We prove that a finite-dimensional Lie algebra $L$ over an algebraically closed field of characteristic $p>0$ is solvable if $L=A+B$ where $[A,A]=0$, $\dim A$, and $B$ is an arbitrary nilpotent subalgebra. We study some more general situation, too. 
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     author = {A. I. Kostrikin},
     title = {A solvability criterion for a finite-dimensional {Lie} algebra},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {5--8},
     publisher = {mathdoc},
     number = {2},
     year = {1982},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a1/}
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A. I. Kostrikin. A solvability criterion for a finite-dimensional Lie algebra. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 5-8. http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a1/