Extrinsic properties of automorphism groups of formal groups

We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then that series is already an automorphism. The second is that the group of automorphisms is its own normalizer in the group of all invertible series over the ground field. A consequence of these results is that a formal group law in positive characteristic is determined by any one of its nontorsion automorphisms.