Title page for ETD etd-05172011-140313


Type of Document Master's Thesis
Author Karcher, Kelli Marie
Author's Email Address kkarcher@vt.edu
URN etd-05172011-140313
Title The Space of Left Orders on a Group
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Linnell, Peter A. Committee Chair
Brown, Ezra A. Committee Member
Loehr, Nicholas A. Committee Member
Keywords
  • Heisenberg group
  • left orderable groups
Date of Defense 2011-05-03
Availability restricted
Abstract
The study of orderable groups is a topic that is all too often overlooked as a topic in algebra.

The subject of orderable groups is a field of study which is directly associated with algebraic group theory, algebraic topology, and set theory. This paper will act as a guide into the world of orderable groups. It begins by enlightening the reader to the fundamental axioms of orderable groups, as well as, noting various important groups on which orders are often considered. We will then consider more interesting groups, on which the placement of orders is considered less often.

After considering the orderings placed on various groups, we wish to consider in further detail the topologies of the sets of these orders. In particular, it is important to consider whether the set of orders placed on a particular group is finite or uncountable. We prove the latter by creating a homeomorphism from the group to the Cantor set, a set which is known for its uncountability.

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