Congruence modularity implies cyclic terms for finite algebras

An n-ary operation f : An → A is called cyclic if it is idempotent and f(a1, a2, a3, . . . , an) = f(a2, a3, . . . , an, a1) for every a1, . . . , an ∈ A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.