Balanced identity that describes n-ary group isotopes in the class of all n-ary quasigroups - Kirnasovskii, O. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We obtain a balanced identity that holds in a primitive n-ary quasigroup if and only if the polyadic quasigroup associated with the considered primitive n-ary quasigroup is a polyadic group isotope.