Abstract
The cohomology theory of Lie algebras has been developed mainly as an example of general homological algebra. Little use has been made of this theory for the proof of structure theorems. The principal cohomology theorem which makes use of the special properties of Lie algebras is the WHITEHEAD lemma. This deals with semi-simple algebras, and is used to prove the theorem of LEvI-MALCEV 1. In this paper, we investigate conditions for the cohomology of a soluble Lie algebra to be trivial, and use these to obtain Lie algebra analogues of some well-known theorems on the structure of finite groups.
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