Type of Document Master's Thesis Author Karcher, Kelli Marie Author's Email Address email@example.com 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 AbstractThe 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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