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|Title: ||A k-Conjugacy Class Problem|
|Authors: ||Roberts, Collin|
|Keywords: ||group theory|
locally finite group
universal locally finite group
existentially closed 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|
|Appears in Collections:||Electronic Theses and Dissertations (UW)|
Faculty of Mathematics Theses and Dissertations
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