Abstract
dc:description.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.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Karcher, Kelli Marie
- Chair dc:contributor.committeechair
-
- Linnell, Peter A.
- Committee members dc:contributor.committeemember
-
- Loehr, Nicholas A.
- Brown, Ezra A.
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-05172011-140313
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/42700