BYU

Abstract by Lindsay Soelberg

Personal Infomation


Presenter's Name

Lindsay Soelberg

Co-Presenters

None

Degree Level

Masters

Co-Authors

None

Abstract Infomation


Department

Mathematics

Faculty Advisor

Pace Nielsen

Title

Group Algebras of Torsion-free Groups: Zero Divisors or not?

Abstract

Given a group G and a field F let F[G] denote the group algebra. There is an old conjecture from Kaplansky dating back to 1956 that says if G is torsion-free then F[G] has no zero divisors.  It is easy to show that this conjecture is true when G is a unique product group.  It is possible to exhaustively search for torsion-free groups without the unique product property on sets of limited size.  Searching for groups with no unique products is a first step in finding a counterexample to this conjecture.  This comprehensive inquiry has shown that if A*B has no unique product where A,B are subsets of G, then |A| + |B| > 12.  Further, there exist sets A,B that are subsets of G with |A| = |B| = 8 which has no unique product.