Vol. 34, No. 1, 1970

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Frattini subalgebras of a class of solvable Lie algebras

Ernest Lester Stitzinger

Vol. 34 (1970), No. 1, 177–182

In this paper the Lie algebra analogues to groups with property E of Bechtell are investigated. Let χ be the class of solvable Lie algebras with the following property: if H is a subalgebra of L, then ϕ(H) ϕ(L) where ϕ(L) denotes the Frattini subalgebra of L; that is, ϕ(L) is the intersection of all maximal subalgebras of L. Groups with the analogous property are called E-groups by Bechtell. The class X is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal N of L χ be the Frattini subalgebra of L. Only solvable Lie algebras of finite dimension are considered here.

Mathematical Subject Classification
Primary: 17.30
Received: 8 October 1969
Published: 1 July 1970
Ernest Lester Stitzinger