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A New Subgroup Chain For The Finite Affine Group, David Alan Lingenbrink Jr.
A New Subgroup Chain For The Finite Affine Group, David Alan Lingenbrink Jr.
HMC Senior Theses
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.