Lattices With a Given Abstract Group of Automorphisms

Abstract

The problem of finding a lattice with a given abstract group of automorphisms has been solved by Garrett Birkhoff who proved that for any group of order g there exists a distributive lattice with at most elements. That this number can be somewhat reduced by modifications of Birkhoff's original procedure has already been shown by the author; it turns out, however, that it remains rather high for finite groups of relatively low order.