| We determine the clone of a finite idempotent algebra A that is not simple and has a unique nontrivial subalgebra S with more than two elements. Under these conditions, the proper subalgebras and the quotient algebra of A are finite idempotent strictly simple algebras of size at least 3 and it is known that such algebras are either affine, quasiprimal, or of a third classification. We focus on the first two cases. By excluding binary edge blockers from the relational clone when S is affine and by excluding ternary edge blockers from the relational clone together with an additional condition on the subuniverses of A2 when S is quasiprimal, we give a nice description of the generating set of the relational clone of A . Thus, by the Galois connection between operations and relations, we determine the clone of A . |
