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.
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 ...
McGee, Sean Liam (University of Waterloo, 2010-08-11)The majority of typically sized galaxies in the local Universe reside in a common dark matter halo with other similar galaxies known as a galaxy group. However, this was not always the case. Nine billion years ago, when ...