A k-Conjugacy Class Problem
MetadataShow full item record
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.
Cite this version of the work
Collin Roberts (2007). A k-Conjugacy Class Problem. UWSpace. http://hdl.handle.net/10012/3208
Showing items related by title, author, creator and subject.
Effects of task variation and communication medium on group performance in small groups: a comparison between FTF and CMC groups Gonzalez, Paola (University of Waterloo, 2009-10-02)Organizational support for cooperative work has been shifted from using Face-to-Face (FTF) communication in collocated groups to using Communication-Mediated-Communication (CMC) in dispersed groups. This new and growing ...
Chen, Lin (University of Waterloo, 2010-04-30)Organizations today face complex problems requiring individuals to work in groups to develop insightful solutions efficiently through coordination, sharing, and integration of distributed knowledge. However, very little ...
Li, Francis (University of Waterloo, 2016-09-06)Robotics and artificial intelligence have seen drastic advancements in technology and algorithms over the last decade. Computer vision algorithms play a crucial role in enabling robots and machines to understand their ...