Closure conditions in the nets
In an absolute space with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that is a linear space with hyperbolic incidence structure, the addition is not associative. is a K-loop or a Bruck loop.