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.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1064 |
| Date | 01 January 2014 |
| Creators | Lingenbrink, David Alan, Jr. |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
| Rights | © 2014 David Lingenbrink |
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