Abstract. We prove that every three-element Mal'tsev algebra is determined, up to term equivalence, by its subalgebras, congruences, internal homomorphisms, labels of prime quotients (in the sense of tame congruence theory), and in certain special cases, by subalgebras of its cube. Thus there exist only finitely many three-element Mal'tsev algebras, up to term equivalence.

AMS Subject Classification (1991): 08A40, 08B05, 08A20

Received December 21, 2000, and in final form April 20, 2005. (Registered under 5883/2009.)