Finite Axiomatisability of Subdirectly Irreducible Members of Certain Nilpotent Varieties

Abstract

Let $\mathcal{V}$ be a congruence permutable variety generated by a finite nilpotent algebra $\mathbf{A}$. If $\mathbf{A}$ is a product of algebras of prime power order, then the class $\mathcal{V}_\text{si}$ of subdirectly irreducible members of $\mathcal{V}$ can be axiomatised by a finite set of elementary sentences.