Abstract. We show that a minimal clone has a nontrivial abelian representation if and only if it is isomorphic to a minimal subclone of a finite cyclic group. As an application, we show that a minimal clone contains a Mal'cev operation if and only if it is isomorphic to the clone of idempotent operations of a group of prime order.

AMS Subject Classification (1991): 08B05

Keyword(s): Varietal product, tame congruence theory, transfer principles

Received November 16, 1994, and in revised form February 20, 1995. (Registered under 5672/2009.)