Show simple item record

dc.contributor.authorRoberts, Collin 14:53:39 (GMT) 14:53:39 (GMT)
dc.description.abstractIn 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.publisherUniversity of Waterlooen
dc.subjectgroup theoryen
dc.subjectk-conjugacy classen
dc.subjectlocally finite groupen
dc.subjectuniversal locally finite groupen
dc.subjectexistentially closed groupen
dc.subjectEngel groupen
dc.titleA k-Conjugacy Class Problemen
dc.typeMaster Thesisen
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages