Let $k$ be an infinite field, and let $L$ be a finite-dimensional Lie algebra over $k$. Then there exists a Lie subalgebra $H \subset L$ such that $H$ is nilpotent and self-normalizing, meaning
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\begin{align*}
N_L(H) := \{z \in L : [z,h] \in H \text{ for every } h \in H\} = H.
\end{align*}
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Equivalently, every finite-dimensional Lie algebra over an infinite field has a Cartan subalgebra.