Geodesic
Loops as Invariant Sections in Groups, and their Geometry
Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 1027-1056

Voir la notice de l'article provenant de la source Cambridge University Press

We investigate left conjugacy closed loops which can be given by invariant sections in the group generated by their left translations. These loops are generalizations of the conjugacy closed loops introduced in [13] just as Bol loops generalize Moufang loops. The relations of these loops to common classes of loops are studied. For instance on a connected manifold we construct proper topological left conjugacy closed loops satisfying the left Bol condition but show that any differentiable such loop must be a group. We show that the configurational condition in the 3-net corresponding to an isotopy class of left conjugacy closed loops has the same importance in the geometry of 3-nets as the Reidemeister or the Bol condition.
DOI : 10.4153/CJM-1994-059-8
Mots-clés : 20N05, 20B99, 22E99, 05B30, 51A99, 53C30 
Nagy, Péter T.; Strambach, Karl. Loops as Invariant Sections in Groups, and their Geometry. Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 1027-1056. doi: 10.4153/CJM-1994-059-8
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