Title page for ETD etd-05032007-212457

Type of Document Master's Thesis
Author Carter, William Paul
URN etd-05032007-212457
Title Non-unique Product Groups on Two Generators
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Linnell, Peter A. Committee Chair
Floyd, William J. Committee Member
Green, Edward L. Committee Member
  • group ring
  • unique product property
Date of Defense 2007-04-26
Availability unrestricted
The main purpose of this paper is to better understand groups that do not have the unique product property. In particular, the goal is to better understand Promislow's example, G, of such a group. In doing so, we will develop methods for generating examples of other sets that do not have the unique product property. With these methods we can show that there exists other distinct 14 element, square, non-unique product sets in G that are not inversions or translations. Also, this paper answers the question as to whether every non-unique product set can have only 14 elements in the negative by producing a 17 element square n.u.p. set. The secondary purpose of this paper is to demonstrate that in the group ring K[G], there are no units of support size 3.
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