Regular orderings of left orderable groups

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dc.contributor.authorKapoostinsky, Dana
dc.contributor.examiningcommitteeCooper, Susan (Mathematics)
dc.contributor.examiningcommitteeKucera, Thomas (Mathematics)
dc.contributor.supervisorClay, Adam
dc.date.accessioned2024-09-05T18:51:33Z
dc.date.available2024-09-05T18:51:33Z
dc.date.issued2024-08-20
dc.date.submitted2024-08-21T00:55:43Zen_US
dc.degree.disciplineMathematics
dc.degree.levelMaster of Science (M.Sc.)
dc.description.abstractThis thesis explores the left orderings of finitely generated torsion-free abelian groups and finitely generated torsion-free nilpotent groups through the lens of computational complexity theory. We demonstrate that both types of groups admit regular left orderings. In chapters 2 and 3, the preliminaries of orderable groups and formal languages are introduced. In Chapter 4, we establish that the set of regular left orderings of $(\mathbb{Z}^n,+)$ is dense within the space of left orderings, $\mathrm{LO}(\mathbb{Z}^n)$. This result is achieved by approaching the problem from a geometric perspective and applying techniques from lattice theory. In Chapter 5, we extend this finding to finitely generated torsion-free nilpotent groups to obtain an analogous result, that is, we show that the set of regular left orderings of a finitely generated torsion-free nilpotent group is also dense within its space of orderings.
dc.description.noteOctober 2024
dc.identifier.urihttp://hdl.handle.net/1993/38519
dc.language.isoeng
dc.rightsopen accessen_US
dc.subjectorderable groups
dc.subjectnilpotent
dc.subjectabstract algebra
dc.subjecttopology
dc.subjectspaces of orderings
dc.subjectregular languages
dc.subjectformal languages and automata
dc.subjectmathematics
dc.titleRegular orderings of left orderable groups
dc.typemaster thesisen_US
local.subject.manitobano
project.funder.identifierhttps://doi.org/10.13039/100010318
project.funder.nameUniversity of Manitoba
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