This article is cited in 2 papers

Identities with permutations associated with quasigroups isotopic to groups

G. Belyavskaya

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

Abstract: In this note we select a class of identities with permutations including three variables in a quasigroup $(Q,\cdot)$ each of which provides isotopy of this quasigroup to a group and describe a class of identities in a primitive quasigroup $(Q,\cdot,\backslash,/)$ each of which is sufficient for the quasigroup $(Q,\cdot)$ 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.

Keywords and phrases: Quasigroup, primitive quasigroup, group, abelian group, isotopy of quasigroups, identity.

MSC: 20N05

Received: 09.07.2007

Language: English

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