Sharply 2-transitive groups of projectivities in generalized polygons (Q5936054)

Generalizing results on projectivities of projective planes, the author considers generalized polygons \(\Gamma\) with the property that the group of all projectivities of \(\Gamma\) is sharply 2-transitive [cf. \textit{N. Knarr}, Ars Comb. 25 B, 265-275 (1988; Zbl 0654.51016)]. The main result classifies the generalized quadrangles \(\Gamma\) with this property: \(\Gamma\) is one of three explicitly known finite generalized quadrangles of small order. Furthermore, if \(\Gamma\) is a finite generalized hexagon, then \(\Gamma\) is one of two (mutually dual) generalized hexagons of order (2, 2), or the (unique) generalized hexagon of order (2, 8). Finally, if \(\Gamma\) is a finite generalized octagon, then \(\Gamma\) has order (2, 4) or (4, 2).