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## On commutators of quasigroup congruences. (English)

Authors: Beliavscaia Galina

### Abstract

The commutator $[\alpha ,\beta ]$ of (normal) congruences $\alpha$, $\beta$ on a (quasigroup $Q(\cdot )$) primitive quasigroup $Q(\cdot ,\setminus ,/)$ is studied. Different sets of generators for $[\alpha ,\beta ]$ are shown. In more detail, the commutators $[\alpha ,Q^2]$ and $[Q^2,Q^2]$, playing an important role by the investigation of nilpotency and solvability of algebras from congruence modular varieties, are considered.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova