Non-classical polar unitals in finite Dickson semifield planes

摘要

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.