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On maximal subalgebras and the hypercentre of Lie algebras. (English) Zbl 0871.17017

Hiroshima J. Math. Educ. 5, 51-61 (1997).
Let \(L\) be a Lie algebra (not necessarily finite dimensional) over an arbitrary field. The author derives sufficient conditions for a finitely generated Lie algebra \(L\) to have a nilpotent hypercenter and presents a class of generalized soluble Lie algebras \(L\) such that if \(L\) has a soluble maximal subalgebra, then \(L\) is soluble and such that if \(L\) has a nilpotent maximal subalgebra, then \(L\) is nilpotent-by-abelian-by-nilpotent. It is also proved that if a finitely generated Lie algebra \(L\) has a maximal nilpotent subalgebra, then the Fitting radical of \(L\) is nilpotent.
Reviewer: M.Boral (Adana)

MSC:

17B65 Infinite-dimensional Lie (super)algebras
17B30 Solvable, nilpotent (super)algebras