Some aspects of the finite congruence lattice representation problem
by
Péter P. Pálfy
Eötvös University, Budapest, Hungary

It is perhaps the most famous open problem in universal algebra, whether every finite lattice is isomorphic to the congruence lattice of a finite algebra. It is equivalent to a group theoretic question: Given a finite lattice L, do there exist a finite group G and a subgroup H such that the interval [H;G] in the subgroup lattice of G is isomorphic to L? In this survey talk results of Baddeley, Lucchini and Börner will be discussed. These point towards a negative solution of the general problem. On the other hand, recent constructions by Snow, Hegedüs and the speaker yield representations of certain finite modular lattices as congruence lattices of finite algebras.

Date received: March 25, 2004