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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (54), 2007/

Identities with permutations associated with quasigroups isotopic to groups.

Authors: Beliavscaia Galina

Abstract

In this note we select a class of identities with permutations including three variables in a quasigroup (Q, ·) each of which provides isotopy of this quasigroup to a group and describe a class of identities in a primitive quasigroup (Q, ·, \ , / ) each of which is sufficient for the quasigroup (Q, ·) to be isotopic to a group. From these results it follows that in the identity of V.Belousov [6] characterizing a quasigroup isotopic to a group (to an abelian group) two from five (one of four) variables can be fixed.

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