Oon the Relationship Between the Class of a Lie Algebra and the Classes of Its Subalgebras

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Title:	Oon the Relationship Between the Class of a Lie Algebra and the Classes of Its Subalgebras
Authors:	Suanmali, Suthathip
Advisors:	Robert Martin, Committee Member Kailash Misra, Committee Co-Chair Ernie Stitzinger, Committee Chair Naihuan Jing, Committee Member
Keywords:	nilpotency class nilpotent Lie algebras metabelian
Issue Date:	7-Jun-2007
Degree:	PhD
Discipline:	Mathematics
Abstract:	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.
URI:	http://www.lib.ncsu.edu/resolver/1840.16/3892
Appears in Collections:	Dissertations

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