Date of Award
4-28-2005
Document Type
Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
First Advisor
Dr. James A. Davis
Recommended Citation
Wyman, Brian, "Relative difference sets in 2-groups : a group cohomological viewpoint" (2005). Honors Theses. 472.
https://scholarship.richmond.edu/honors-theses/472
Comments
Relative difference sets (RDS) have been studied at great lengths in Abelian groups. RDSs in 2-groups have connections to constructions of divisible designs, which in turn are in correspondence with binary codes with good error correcting properties. In particular, a recent paper of Galati exhibited a (4, 4, 4, 1)-RDS in a non-Abelian group relative to a normal but not central subgroup, the first known example of such an RDS. We study RDS with this anomaly as our motivation. In our investigations, we found that there is a correspondence between the existence of relative difference sets and the existence of short exact sequences of groups. We appeal to group cohomology to study these short exact sequences and to gain insight into the existence of these RDS.