On PGL(2,q)-invariant unitals embedded in Desarguesian or in Hughes planes

In this paper it is shown that any unital embedded either in PG(2,q2)PG(2,q2) or in the Hughes plane of order q2q2, which is invariant under PGL(2,q)×〈σ〉PGL(2,q)×〈σ〉, where σ is the Frobenius involution, is Hermitian or classical Rosati, respectively.