Abstract

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.