Description:
<jats:p> We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. </jats:p><jats:p> We show that then every congruence preserving function on G (of any finite arity) is a polynomial function. </jats:p>