# A condition on minimal restricted subalgebras of a restricted Lie algebra

Let $$L$$ be a restricted Lie algebra over a field $$F$$ of characteristic $$p>0$$. Assume that the following condition holds:

For every restricted ideal $$I$$ of $$L$$, the minimal restricted subalgebras of $$L/I$$ are pairwise non-isomorphic.

QUESTION: Is $$L$$ necessarily abelian?

I already know that the answer is affirmative if one assumes that $$L$$ is nilpotent.