IMI/Publicaţii/BASM/Ediţii/BASM n.2 (27), 1998/

On commutators of quasigroup congruences. (English)

Authors: Beliavscaia Galina


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.

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