Geodesic
Loop geometries
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 605-616.

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We introduce the construction of the semidirect product of a loop and its associate (or quasigroup) — the group uniquely generated by the loop. For a (left or right) loop the semidirect product is a group acting transitively on the loop so that the loop is provided with the structure of a homogeneous space, the stationary subgroup being its associate. The construction is reversible, viz.: any homogeneous space can be provided with the structure of a loop so that the semidirect product of it with the transassociate is isomorphic with the fundamental group of the homogeneous space and the transassociate is isomorphic with the stationarity group. 
@article{MZM_1972_12_5_a14,
     author = {L. V. Sabinin},
     title = {Loop geometries},
     journal = {Matemati\v{c}eskie zametki},
     pages = {605--616},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a14/}
}
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L. V. Sabinin. Loop geometries. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 605-616. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a14/