FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 3, PAGES 715-737
G. B. Belyavskaya
Abstract
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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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