What is known about the finite congruence lattice representation problem?
by
Péter P. Pálfy
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences

In this survey talk the problem of representing finite lattices as congruence lattices of finite algebras will be considered. I first heard this problem in Ervin's legendary research seminar in 1976. With Pavel Pudlák we proved that the problem is in fact group theoretic, since it is equivalent to the question whether every finite lattice can be represented as an interval in the subgroup lattice of a finite group. Baddeley and Lucchini have reduced the problem to a series of hard questions about finite simple groups. The latest advance was obtained by Ferdinand Börner who further reduced the class of finite groups to be considered.

Date received: June 13, 1999