Construction of unitals in the Hall planes
The aim of the paper is to show a large class of unitals embedded in the Hall planes. This is done by combining several results. First, the author describes the so-called Buekenhout-Metz unitals in Desarguesian projective plane (hermitian curves). Next, she applies techniques of transformation of incidence structures [introduced by P. Quattrocchi and L. A. Rosati], which leaves points and blocks unchanged, but modifies incidence relation, and proves that if the corresponding permutation of the points of a projective plane containing a unital \(\mathcal U\) leaves the point-set of \(\mathcal U\) invariant, then \(\mathcal U\) is also a (point-set of) unital in the modified projective plane. An analogue of this property is also proved for affine planes. Since the Hall planes can be defined by means of suitable transformation of affine plane \(\text{AG}(2,q^2)\), the author obtains (new) unitals embedded in the Hall planes as corresponding modifications of Buekenhout-Metz unitals.
scientific article; zbMATH DE number 806261