Non-unique Product Groups on Two Generators

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Carter, William Paul

Chair dc:contributor.committeechair

• Linnell, Peter A.

Committee members dc:contributor.committeemember

• Floyd, William J.
• Green, Edward L.

• group ring
• unique product property

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05032007-212457

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32153