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Identities with permutations and quasigroups isotopic to groups and to Abelian groups. (English. Russian original) Zbl 1315.20060

Discrete Math. Appl. 23, No. 3-4, 369-384 (2013); translation from Diskretn. Mat. 25, No. 2, 68-81 (2013).
Summary: This paper continues the study of quasigroups isotopic to groups and to Abelian groups. For identities with permutations of a certain kind the notion of the type is introduced; identities with permutations of various types are presented, which characterize quasigroups isotopic to Abelian groups. The approach being used had allowed to establish a number of new unbalanced identities involving four variables in an equasigroup, as well as a number of identities involving three variables in an equasigroup with one nullary operation, each of which characterises a quasigroup isotopic to a group or to an Abelian group.

MSC:

20N05 Loops, quasigroups
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