Point-reflection geometries, geometric K-loops and unitary geometries (Q1377199)

The authors use unitary geometries to show the existence of reflection geometries to which correspond \(K\)-loops with an incidence fibration \(F\) [\textit{E. Zizioli}, J. Geom. 30, 144-156 (1987; Zbl 0632.51019)] where \(F\) consists of proper subloops (other than groups). This is in sharp contrast to ordinary hyperbolic spaces, where those subloops are even commutative subgroups.