Balanced identity that describes <em class="a-plus-plus">n</em>-ary group isotopes in the class of all <em class="a-plus-plus">n</em>-ary quasigroups

Abstract

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.