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It is shown that there is only one class of unitary polarities in the Dickson semifield planes and hence one class of polar unitals in such planes.

We give three proofs, two intrinsic and one extrinsic, that every Dickson–Ganley unital \({\mathcal{U}(\sigma)}\), parametrized by a field automorphism σ, is non-classical if σ is not the identity, extending a result of Ganley’s (Math Z 128:34–42, 1972); we prove that \({\mathcal{U}(\sigma_1)}\) is isomorphic to \({\mathcal{U}(\sigma_2)}\) if and only if σ1 = σ2 or σ1 = σ2−1; and we determine the (design) automorphism group of \({\mathcal{U}(\sigma)}\) as the collineation subgroup of the ambient Dickson semifield plane stabilizing the unital. This contains as a special case the corresponding result of O’Nan’s (J Algebra 20:495–511, 1965) on the classical unital.

Using geometric methods and without invoking deep results from group theory, we prove that a classical unital of even order [math] is characterized by two conditions (I) and (II): (I) is the absence of O’Nan configurations of four distinct lines intersecting in exactly six distinct points; (II) is a notion of parallelism. This was previously proven by Wilbrink (1983), where the proof depends on the classification of finite groups with a split BN-pair of rank [math] .