Unitals in finite Desarguesian planes (Q1610681)

A unital in the Desarguesian projective plane \(\text{PG}(2,q^2)\) is a set of \(q^3+1\) points intersecting each line in either 1 or \(q+1\) points. Such a unital is called classical if it is a non-degenerate Hermitian curve, i.e. the set of absolute points of a non-degenerate Hermitian polarity of \(\text{PG}(2,q^2)\). Among the known characterizations of classical unitals, there are some of group-theoretical nature. The authors add a new characterization to the list: a unital in \(\text{PG}(2,q^2)\) is classical if and only if it is fixed by a linear collineation group of order \(6(q+1)^2\) that fixes no point or line in \(\text{PG}(2,q^2)\).