Geodesic
On definitions of groupoids closely connected with quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 43-54

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Both “existential” and “equational” definitions of binary quasigroups and groupoids closely connected with quasigroups are given. It is proved that a groupoid $(Q,\cdot)$ is a quasigroup if and only if all middle translations of $(Q,\cdot)$ are bijective maps of the set $Q$. 
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     author = {V. A. Shcherbacov},
     title = {On definitions of groupoids closely connected with quasigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {43--54},
     publisher = {mathdoc},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2007_2_a4/}
}
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V. A. Shcherbacov. On definitions of groupoids closely connected with quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 43-54. http://geodesic.mathdoc.fr/item/BASM_2007_2_a4/