New Methods for Finding Non-Left-Orderable and Unique Product Groups

In this paper, we present techniques for proving a group to be non-left-orderable or a unique product group. These methods involve the existence of a mapping from the group to R which obeys a left-multiplication criterion. By determining the existence or non-existence of such a mapping, the desired information about the group can be concluded. As examples, we apply this technique to groups of transformations in hyperbolic 2- and 3- space, and Fibonacci groups.

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

2003

Author dc:creator

• Hair, Steven

Chair dc:contributor.committeechair

• Linnell, Peter A.

Committee members dc:contributor.committeemember

• Farkas, Daniel R.
• Haskell, Peter E.

• Kleinian
• left-orderable
• Fibonacci
• unique product
• Fuchsian

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

etd-12082003-113057

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/9633