Dihedral groups generated by Baer involutions in \(\text{P}\Gamma\text{L}(3,q^2)\) (Q5945002)

It is known that there are seven different intersection patterns for two Baer subplanes in \(\pi = \text{PG}(2,q^2)\) [\textit{R. C. Bose, J. W. Freeman}, and \textit{D. G. Glynn}, On the intersection of two Baer subplanes in a finite projective plane, Util. Math. 17, 65-77 (1980; Zbl 0445.51005)]. One possible intersection configuration is the empty set, and the dihedral group generated by the Baer involutions of two such subplanes was carefully studied by one of the authors in [\textit{J. Ueberberg}, Projective planes and dihedral groups, Discrete Math. 174, No. 1-3, 337-345 (1997; Zbl 0902.51003)]. In the paper under review the authors study the remaining six cases, computing the possible orders for the product of the two Baer involutions associated with the given pair of Baer subplanes. The case when the intersection consists of precisely two points and two lines is studied in detail.