Abstract. We investigate minimal clones of operations on finite sets such that the corresponding algebra is functionally complete. We find that among the 24 isomorphism types of minimal clones over the 3-element set, determined by Béla Csákány, five are functionally complete. One of these minimal clones is generated by a binary operation corresponding to a tournament. We prove that a finite groupoid determined by a tournament is functionally complete, provided it is simple. Since almost all tournaments give rise to simple groupoids, this shows that there are a large number of functionally complete minimal clones.

AMS Subject Classification (1991): 08A40

Keyword(s): functional completeness, minimal clone, tournament

Received July 27, 2007, and in revised form October 16, 2007. (Registered under 6448/2009.)