= Engel normalizer lemma
{c}
{title2=$M\subsetneq N_L(M)$}
If $L$ is a finite-dimensional <Lie algebra> of <nilpotent endomorphisms>, every proper <Lie subalgebra> $M$ is strictly contained in its <normalizer of a Lie subalgebra>. The <Adjoint representation> of $M$ on $L/M$ consists of nilpotent maps by <nilpotence of commutation by a nilpotent endomorphism>. In the inductive proof of <Engel theorem>, the lower-dimensional <Engel lemma> gives a nonzero class $y+M$ with $[M,y]\subseteq M$. A maximal proper $M$ is consequently an <ideal of a Lie algebra> of codimension one.
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