Something about Frattini Subalgebras of a Class of Solvable Lie Algebras
نویسندگان
چکیده
In this paper we consider Q the class of solvable Lie algebras L with the following property: if A is a subalgebra of L, then Φ(A) ⊆ Φ(L) (where Φ(L) denotes the Frattini subalgebra of L;that is Φ(L) is the intersection of all maximal subalgebras of L). The class Q is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal Iof L ∈ Q be the Frattini subalgebra of L. We considered here only solvable Lie algebras of finite dimension.
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