The Space of Left Orders on a Group

Simple item page
dc.contributor.authorKarcher, Kelli Marieen
dc.contributor.committeechairLinnell, Peter A.en
dc.contributor.committeememberLoehr, Nicholas A.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:36:18Zen
dc.date.adate2011-05-18en
dc.date.available2014-03-14T21:36:18Zen
dc.date.issued2011-05-03en
dc.date.rdate2011-05-18en
dc.date.sdate2011-05-17en
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.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05172011-140313en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05172011-140313/en
dc.identifier.urihttp://hdl.handle.net/10919/42700en
dc.publisherVirginia Techen
dc.relation.haspartKarcher_KM_T_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectHeisenberg groupen
dc.subjectleft orderable groupsen
dc.titleThe Space of Left Orders on a Groupen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Karcher_KM_T_2011.pdf
Size:
539.78 KB
Format:
Adobe Portable Document Format
Download

Collections

Masters Theses