A Hamiltonian property for nilpotent algebras

In this paper we show that any finite algebra A satisfying a weak left nilpotence condition has the property that all maximal subuniverses are congruence blocks. Conversely, if every subalgebra of A ² has the property that all maximal subuniverses are congruence blocks, then A satisfies the aforementioned nilpotence condition. Received August 3, 1994; accepted in final form June 27, 1996.