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## Centre and multiplication groups of quasigroups. (English)

Authors: Beliavscaia Galina

### Abstract

In the multiplication group of a quasigroup $Q(\cdot)$ the normal abelian subgroup which acts sharply transitively on every class of the centre congruence of a quasigroup is eliminated. It is proved that if a class of the centre congruence of a quasigroup is a subquasigroup, then it is isotopic to $\Gamma$ and the centre congruence of a quasigroup $Q(\cdot)$ always lies in the centre congruence of a loop principally isotopic to $Q(\cdot)$.