A k-Conjugacy Class Problem
| dc.comment.hidden | The abstract will look better if I can use LaTeX tags around the mathematical symbols. I was not clear from reading the help page that this would work, so I entered it as plain text. At your convenience, please advise whether LaTeX tags are allowed for the abstract. Thanks! | en |
| dc.contributor.author | Roberts, Collin | |
| dc.date.accessioned | 2007-09-07T14:53:39Z | |
| dc.date.available | 2007-09-07T14:53:39Z | |
| dc.date.issued | 2007-09-07T14:53:39Z | |
| dc.date.submitted | 2007-08-15 | |
| dc.description.abstract | In any group G, we may extend the definition of the conjugacy class of an element to the conjugacy class of a k-tuple, for a positive integer k. When k = 2, we are forming the conjugacy classes of ordered pairs, when k = 3, we are forming the conjugacy classes of ordered triples, etc. In this report we explore a generalized question which Professor B. Doug Park has posed (for k = 2). For an arbitrary k, is it true that: (G has finitely many k-conjugacy classes) implies (G is finite)? Supposing to the contrary that there exists an infinite group G which has finitely many k-conjugacy classes for all k = 1, 2, 3, ..., we present some preliminary analysis of the properties that G must have. We then investigate known classes of groups having some of these properties: universal locally finite groups, existentially closed groups, and Engel groups. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/3208 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | group theory | en |
| dc.subject | k-conjugacy class | en |
| dc.subject | locally finite group | en |
| dc.subject | universal locally finite group | en |
| dc.subject | existentially closed group | en |
| dc.subject | Engel group | en |
| dc.subject.program | Pure Mathematics | en |
| dc.title | A k-Conjugacy Class Problem | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |