Projective planes and dihedral groups

In the present article we shall show that any two disjoint Baer subplanes of PG(2,q(2)) are contained in exactly one Singer-Baer partition. Given two disjoint Baer subplanes of P = PG(2,q(2)) with Baer involutions tau(0) and tau(1) we shall see that delta := tau(0) tau(1) is a projective collineation whose order is a divisor of q(2)-q + 1. If o(delta) = q(2)-q+1, then the point orbits of P under the action of (delta) are so-called Kestenband arcs.