Congruence Lattices of Finite Algebras a Dissertation Submitted to the Graduate Division of the University of Hawai‘i at Mānoa in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics

An important and long-standing open problem in universal algebra asks whether every finite lattice is isomorphic to the congruence lattice of a finite algebra. Until this problem is resolved, our understanding of finite algebras is incomplete, since, given an arbitrary finite algebra, we cannot say whether there are any restrictions on the shape of its… (More)