  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.
