Engel's Theorem states that a Lie algebra is nilpotent if and only if every derivation is nilpotent. This theorem provides a crucial link between the concepts of nilpotency and the structure of Lie algebras, showing that the behavior of derivations can reveal important properties about the algebra itself. Engel's Theorem emphasizes the significance of nilpotent elements in the study of Lie algebras, allowing mathematicians to better understand their structure and behavior through derivations.
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