Embedding of orthogonal Buekenhout-Metz unitals in the Desarguesian plane of order q2

Gábor Korchmáros, Alessandro Siciliano

Abstract


A unital, that is a 2-(q3 + 1, q + 1, 1) block-design, is embedded in a projective plane π of order q2 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 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 U into the Desarguesian plane of order q2. In this paper we extend this uniqueness result to all unitals which are isomorphic, as block-designs, to orthogonal Buekenhout-Metz unitals.


Keywords


Unital, embedding, finite Desarguesian plane

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DOI: https://doi.org/10.26493/1855-3974.1681.4ec

ISSN: 1855-3974

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