Geodesic
Reflection loops of spaces with congruence and hyperbolic incidence structure
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 303-320.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 20N05, 51A25, 51D99, 51E14, 51F15
Keywords: ordered space with congruence; point reflection; Bol loop; K-loop 
@article{CMUC_2004__45_2_a11,
     author = {Kreuzer, Alexander},
     title = {Reflection loops of spaces with congruence and hyperbolic incidence structure},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {303--320},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2004},
     mrnumber = {2075279},
     zbl = {1101.20044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a11/}
}
TY  - JOUR
AU  - Kreuzer, Alexander
TI  - Reflection loops of spaces with congruence and hyperbolic incidence structure
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2004
SP  - 303
EP  - 320
VL  - 45
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a11/
LA  - en
ID  - CMUC_2004__45_2_a11
ER  - 
%0 Journal Article
%A Kreuzer, Alexander
%T Reflection loops of spaces with congruence and hyperbolic incidence structure
%J Commentationes Mathematicae Universitatis Carolinae
%D 2004
%P 303-320
%V 45
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a11/
%G en
%F CMUC_2004__45_2_a11
Kreuzer, Alexander. Reflection loops of spaces with congruence and hyperbolic incidence structure. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 303-320. http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a11/