Congruence Lattices of Finite Algebras

Congruence Lattices of Finite Algebras
by William DeMeo

Publisher: arXiv 2012
Number of pages: 130

Description:
In this work, we review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist without actually constructing them. By combining these well known methods with a new method we have developed, we prove that with one possible exception every lattice with at most seven elements is isomorphic to the congruence lattice of a finite algebra.