Abelian Algebras and the Hamiltonian Property

In this paper we show that a nite algebra A is Hamiltonian if the class HS(A A) consists of Abelian algebras. As a consequence, we conclude that a locally nite variety is Abelian if and only if it is Hamilto-nian. Furthermore it is proved that A generates an Abelian variety if and only if A A 3 is Hamiltonian. An algebra is Hamiltonian if every nonempty subuniverse is a block of some congruence on the algebra and an algebra is Abelian if for every term t(x; y), the implication t(x; y) = t(x; z) ! t(w; y) = t(w; z) holds. Thus, locally nite Abelian varieties have deenable principal congruences, enjoy the congruence extension property, and satisfy the RS-conjecture.