Non-singular derivations of solvable Lie algebras in prime characteristic

Abstract

We study solvable Lie algebras in prime characteristic p that admit non-singular derivations. We show that Jacobson's Theorem remains true if the quotients of the derived series have dimension less than p. We also study the structure of Lie algebras with non-singular derivations in which the derived subalgebra is abelian and has codimension one. The paper presents some new examples of solvable, but not nilpotent, Lie algebras of derived length 3 with non-singular derivations.