Embedding of orthogonal Buekenhout-Metz unitals in the Desarguesian plane of order qsup2 - Csajbók, Bence (Ars mathematica contemporanea, 2019)
A unital, that is a ?$2-(q^3 + 1, q + 1, 1)$? block-design, is embedded in a projective plane ?$π$? of order ?$q^2$? if its points are points of ?$π$? and its blocks are subsets of lines of ?$π$?, the point-block incidences being the same as in ?$π$?. Regarding unitals ?$\mathcal U$? which are isomorphic, as a block-design, to the classical unital, T. Szőnyi and the authors recently proved that the natural embedding is the unique embedding of ?$\mathcal U$? into the Desarguesian plane of order ?$q^2$?. In this paper we extend this uniqueness result to all unitals which are isomorphic, as block-designs, to orthogonal Buekenhout-Metz unitals.
Keywords: embedding; finite Desarguesian plane; končna Desarguesova ravnina; unital; vložitev