Title Some results on the action of the automorphism group of a finite topological space Type Presentation Keywords Finite topological space, Automorphism group, Transitive action, Primitive action. Abstract Let X be a finite topological space. In this paper, we show that if the action of Aut(X) is transitive and X is a connected space then X has the trivial topology. Also if the action of Aut(X) is primitive then X has the trivial topology or discrete topology. Researchers hamidreza dorbidi (First researcher)