Automorphism groups of finite posets

Abstract

For any finite group G, we construct a finite T_0 poset (or equivalently, a finite -space) X , whose group of automorphisms is isomorphic to G . If the order of the group is n and it has r generators, X has n(r+2) points. This construction improves previous results by G. Birkhoff and M.C. Thornton. The relationship between automorphisms and homotopy types is also analyzed.