Subinvariance in Solvable Lie Algebras

In a recent paper, Wielandt has continued his investigation of subnormal subgroups. Since the analogous concept is also of interest in Lie algebras, this note considers the Lie algebra counterparts to Wielandt's results. Generally the results do not carry over to all Lie algebras, but do hold in the solvable case. In order to state the main results, several definitions are needed and consequently we begin by listing some of the consequences. All Lie algebras considered here are finite dimensional over a field.