Identities with permutations associated with quasigroups isotopic to groups

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.