|Polynomial clones on groups of order pq
Aichinger, Erhard; Mayr, P.
Acta Math. Hungar., 114, no. 3 (2007), 267--285
For two distinct primes p, q, we describe those clones on a set of size pq that contain a given group operation and all constants operations. We show that each such clone is determined by congruences and commutator relations. Thus we obtain that there is only a finite number of such clones on a fixed set.