## Alexander Kreuzer Reflection loops of spaces with congruence and hyperbolic incidence structure

Comment.Math.Univ.Carolinae 45,2 (2004) 303-320.

Abstract:In an absolute space $(P, \frak L, \equiv , \alpha )$ 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 $(P, \frak L, \alpha )$ is a linear space with hyperbolic incidence structure, the addition is not associative. $(P,+)$ is a K-loop or a Bruck loop.

Keywords: ordered space with congruence, point reflection, Bol loop, K-loop
AMS Subject Classification: 51D, 20N05