Solvable Lie A-algebras

A finite-dimensional Lie algebra L over a field F is called an A-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an A-group: a finite group with the property that all of its Sylow subgroups are abelian. These groups were first studied in the 1940s by Philip Hall, and are still studied today. Rather less is known about A-algebras, though they have been studied and used by a number of authors. The purpose of this paper is to obtain more detailed results on the structure of solvable Lie A-algebras.