FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 3, PAGES 715-737

Assiociants and the commutant of a quasigroup

G. B. Belyavskaya

Abstract

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Six normal congruences called associants or commutator-associants are defined in a quasigroup $Q($× ) 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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