Determining synchronization of certain classes of primitive groups of affine type
Date
2022
Authors
Story, Dustin, author
Hulpke, Alexander, advisor
Adams, Henry, committee member
Buchanan, Norm, committee member
Gillespie, Maria, committee member
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Abstract
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 non-synchronizing. 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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Subject
primitive
synchronizing
synchronization
affine