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Assiociants and the commutant of a quasigroup

G. B. Belyavskaya

Institute of Mathematics, Academy of Sciences of Moldova

Abstract: 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.

UDC: 512.548

Received: 01.11.1995

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