Geodesic
Assiociants and the commutant of a quasigroup
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 715-737

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Six normal congruences called associants or commutator-associants are defined in a quasigroup $Q(\cdot)$ by means of associators of two types and commutators. It is proved that these congruences are verbal congruences corresponding to different types of quasigroups linear over groups. As a consequence a description of generators of the quasigroup commutant is obtained. Behaviour of the considered congruences under isotopy of quasigroups and in the left-distributive (distributive) quasigroups is investigated. 
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     author = {G. B. Belyavskaya},
     title = {Assiociants and the commutant of a quasigroup},
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     volume = {3},
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     language = {ru},
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G. B. Belyavskaya. Assiociants and the commutant of a quasigroup. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 715-737. http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a5/