Unitals and inversive planes
Let \({\mathcal P}\) be a translation plane of dimension at most 2 over its kernel \(\text{GF} (q)\), and let \(U\) be a Buekenhout-Metz unital in \({\mathcal P}\). The authors show that \(U\) has an associated \(2-(q^2, q+1,q)\) design which is the point-residual of an inversive plane. This generalizes work by \textit{H. Wilbrink} [Lect. Notes Pure Appl. Math. 82, 445-454 (1983; Zbl 0507.05014)], \textit{R. Baker} and \textit{G. Ebert} [J. Comb. Theory, Ser. A 60, No. 1, 67-84 (1992; Zbl 0783.05031)], and \textit{G. Ebert} [Eur. J. Comb. 13, No. 2, 109-117 (1992; Zbl 0758.51006)]. The authors of this investigation use the geometry inherent in the Buekenhout-Metz unital construction, while Wilbrink' work is synthetic and the work of Baker and Ebert uses coordinates.
scientific article; zbMATH DE number 1000343