Finite lattices as relative congruence lattices of finite algebras

Abstract.

Let A be a finite algebra and ${\mathcal{Q}}$ a quasivariety. By ${\rm Con}_{{\mathcal{Q}}}$ A is meant the lattice of congruences θ on A with $A/\theta \in {\mathcal{Q}}$. For any positive integer n, we give conditions on a finite algebra A under which for any n-element lattice L there is a quasivariety ${\mathcal{R}}$ such that ${\rm Con}_{R} A \cong L$.