Definition 1

Tag 09Y1, permanent. Cite it as [Bourbaki, Tag 09Y1].

Lie Groups and Lie Algebras, chapter I, § 5. Solvable Lie algebras

A Lie algebra $g$ is called solvable if its kth derived algebra $D^k g$ is zero for sufficiently large $k$ .

A nilpotent Lie algebra is solvable.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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