Involutory homologies on affine planes: The conclusion (Q2639337)

The author finishes his investigations [cf. ibid. 57, 37-55 (1987; Zbl 0638.51003) and Boll. Unione Mat. Ital., VII. Ser., A1, 383-386 (1987; Zbl 0642.51002)] on projective planes \({\mathfrak P}=(P,{\mathcal L})\) where there is a finite subgroup G of Aut(\({\mathfrak P})\) fixing a nonincident point line (z,L) such that G is generated by a normal set R of reflections with (P1) \(\forall (p,X)\in P\times {\mathcal L}\) with \(p\not\in X\), \(Syl_ 2(G(p,X))\) contains at most one involution. In the two previous papers the author determined the structure of factor groups \(G/O_{2',2}(G)\) and G/O(G) in the case \(G=O_{2',2}(G)\). Here he studies the structure of \(O_{2',2}(G)/O(G)\) in the general case.