Automorphisms of the Nottingham Group

Let K be a finite field of characteristic p ≥ 5. The Nottingham group over K is the group of normalised automorphisms of the local field K((t)). In this paper we determine the automorphism group of ; in particular we show that every automorphism of the Nottingham group is standard. We also give a complete description of the conjugacy classes of elements of order p in .