|
UWSpace >
University of Waterloo >
Electronic Theses and Dissertations (UW) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10012/3208
|
| Title: | A k-Conjugacy Class Problem |
| Authors: | Roberts, Collin |
| Keywords: | group theory
k-conjugacy class
locally finite group
universal locally finite group
existentially closed group
Engel group |
| Approved Date: | 7-Sep-2007 |
| Date Submitted: | 15-Aug-2007 |
| 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. |
| Program: | Pure Mathematics |
| Department: | Pure Mathematics |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/3208 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
|
This item is protected by original copyright
|
All items in UWSpace are protected by copyright, with all rights reserved.
|
