Simple modular Lie algebras with a solvable maximal subalgebra

This paper contains a proof of the following
Theorem. {\it Let $\mathfrak L$ be a simple Lie algebra which is finite dimensional over an algebraically closed field $K,$ where $\operatorname{char}K=p>3,$ and which contains a solvable maximal subalgebra $\mathfrak L_0$ acting irreducibly on the space $\mathfrak L/\mathfrak L_0$. Then $\mathfrak L$ is either the classical algebra $A_1$ or the Zassenhaus algebra $W_1(n)$.}
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