A non-classical unital of order four with many translations

Abstract

We give a general construction for unitals of order q admitting an action of SU(2,q). The construction covers the classical Hermitian unitals, Grüning’s unitals in Hall planes and at least one unital of order four where the translation centers fill precisely one block. For the latter unital, we determine the full group of automorphisms and show that there are no group-preserving embeddings into (dual) translation planes of order 16.