On the Construction of Partially Ordered Systems with a Given Group of Automorphisms
Robert Frucht · American Journal of Mathematics · 1950
In a recent paper 1 G. Birkhoff showed that when an abstract group of g elements is given (g being a finite number or an infinite cardinal number), there exists always a partially ordered system with g2 + g elements whose group of automorphisms is simply isomorphic to the given group. I shall prove the following result for the case of a finite g: There can be found a partially ordered system with only (n + 2)g elements whose group of automorphisms is simply isomorphic to a given abstract group of finite order g, when this group can be generated by n of its elements; and if n > 2, still fewer elements will be needed.