On the Relationship between the Class of a Lie Algebra and the Classes of its Subalgebras

SUANMALI, SUTHATHIP. On the Relationship between the Class of a Lie Algebra and the Classes of its Subalgebras. (Under the direction of Ernie L. Stitzinger.) A classical nilpotency result considers finite p-groups whose proper subgroups all have class bounded by a fixed number n. We consider the analogous property in nilpotent Lie algebras. In particular, we investigate whether this condition puts a bound on the class of the Lie algebra. Some p-group results and proofs carry over directly to the Lie algebra case, some carry over with modified proofs and some fail. For the final of these cases, a certain metabelian Lie algebra is constructed to show a case when the p-groups and Lie algebra cases differ. ON THE RELATIONSHIP BETWEEN THE CLASS OF A LIE ALGEBRA AND THE CLASSES OF ITS SUBALGEBRAS by SUTHATHIP SUANMALI A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy MATHEMATICS Raleigh, North Carolina 2007