This article is cited in 3 papers

On some quasi-identities in finite quasigroups

G. Belyavskaya, A. Diordiev

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

Abstract: In this article we consider some quasi-identities in quasigroups, in particular, quasi-identities connected with parastrophic orthogonality of a quasigroup. We also research some quasi-identities in quasigroups (in loops) with one parameter $\delta$ ($\delta$-quasi-identities) which arose by the study of detecting coding systems such as check character systems in [6] (see also [5, 7]), establish equivalence of such quasi-identities, connection of some of them with orthogonality of quasigroups and give a number of examples of finite quasigroups with such $\delta$-quasi-identities.

Keywords and phrases: Quasigroup, loop, group, automorphism, quasi-identity, orthogonality, parastrophe.

MSC: 20N05, 94B60

Received: 12.12.2005

Language: English

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