Some natural subgroups of the Nottingham group

Abstract

The Nottingham group can be described as the group of normalized automorphisms of the ring Fp[[t]], namely, those automorphisms acting trivially on tFp[[t]]/t2Fp[[t]]. In this paper we consider certain proper subgroups of the Nottingham group. We prove that these subgroups are identical to their normalizers and that some of them are isomorphic to the Nottingham group.