Automorphism groups of posets with forbidden subposets

AbstractWe show that there exists a finite set S of finite posets such that the following holds. Whenever, (Y,⩽) is not isomorphic to a member of S and it is not trivially ordered then for every finite group G there exists a finite poset (X,⩽) which has no induced subposet isomorphic to (Y,⩽) such that G is isomorphic to the automorphism group of (X,⩽). For some members (Y,⩽) of S we give necessary and sufficient conditions for a group G to be isomorphic to the automorphism group of a finite poset (X,⩽) which has no induced subposet (Y,⩽). This includes the classification of the automorphism groups of finite interval orders and series- parallel posets