Regular incidence permutation sets and incidence quasigroups (Q1281739)

The authors consider incidence spaces (also called linear spaces) together with a set of collineations that operate regularly on the point set of the space. Then the point set of the space can be turned into a quasigroup, thus generalizing the notion of ``incidence group'' coined by the first author in the early sixties. In particular, the authors pay attention to the special case that the distinguished set of collineations consists of ``weak dilatations''. A weak dilatation is, by definition, a collineation such that each line is either disjoint or identical with its image line. Also special cases arising from kinematic spaces, affine spaces and hyperbolic planes are discussed.