Open Access Senior Thesis
Bachelor of Science
© 2014 David Lingenbrink
The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
Lingenbrink, David Alan Jr., "A New Subgroup Chain for the Finite Affine Group" (2014). HMC Senior Theses. 55.