Title: Determining synchronization of certain classes of primitive groups of affine type

Advisor:  Dr. Alexander Hulpke

Committee:  Dr. Maria Gillespie, Dr. Henry Adams, Dr. Norman Buchanan

The class of permutation groups includes 2-homogeneous groups, synchronizing groups, and primitive groups. Moreover, 2-homogeneous implies synchronizing, and synchronizing in turn implies primitivity. A complete classification of synchronizing groups remains an open problem. Our search takes place amongst the primitive groups, looking for examples of synchronizing and nonsynchronizing. Using a case distinction from Aschbacher classes, our main results are constructive proofs showing that three classes of primitive affine groups are nonsynchronizing.

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