Non-classical polar unitals in finite Dickson semifield planes

We give three proofs, two intrinsic and one extrinsic, that every Dickson–Ganley unital U ( σ ) , 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 U ( σ 1 ) is isomorphic to U ( σ 2 ) if and only if σ 1 = σ 2 or σ 1 = σ 2 −1 ; and we determine the (design) automorphism group of U ( σ ) 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.