## 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

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