Geodesic
Associators, commutators and the linearity of a quasigroup
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 116-125.

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In a quasigroup $Q(\cdot)$ the associators of two types and the commutators with respect to an arbitrary fixed element $h\in Q$ ($h$-associators and $h$-commutators) are introduced. Their connection with the normal subsets (subquasigroups) is determined, and the characterization of the left (right) $h$-kernel, of the $h$-centre of quasigroups and of various linear (over group) quasigroups is given in terms of $h$-associators and $h$-commutators. 
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     author = {G. B. Belyavskaya},
     title = {Associators, commutators and the linearity of a quasigroup},
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     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_4_a9/}
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G. B. Belyavskaya. Associators, commutators and the linearity of a quasigroup. Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 116-125. http://geodesic.mathdoc.fr/item/DM_1995_7_4_a9/