A group theoretic characterization of classical unitals
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 1, pp. 33-43.

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Summary: Let $G$ be the group of projectivities stabilizing a unital $U$ mathcalU in $PG(2, q ^{2})$. In this paper, we prove that $U$ mathcalU is a classical unital if and only if there are two points in $U$ mathcalU such that the stabilizer of these two points in $G$ has order $q ^{2} - 1$.
Keywords: keywords unitals, Hermitian curves, Reed-muller codes
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Donati, Giorgio; Durante, Nicola. A group theoretic characterization of classical unitals. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/JAC_2012__36_1_a6/