Some hereditarily just infinite subgroups of the Nottingham Group

Abstract

This work examines the commutator structure of some closed subgroups of the wild group of automorphisms of a local field with perfect residue field, a group we call $\Cal J.$ In particular, we establish a new approach to evaluating commutators in $\Cal J$ and using this method investigate the normal subgroup structure of some classes of index subgroups of $\Cal J$ as introduced by Klopsch. We provide new proofs of Fesenko\rq s results that lead to a proof that the torsion free group $T=\{t+{\sum }_{k\ge 1}{a}_k{t}^{qk+1}:a_k\in {\mathbb{F}}_p\}$ is hereditarily just infinite, and by extending his work, we also demonstrate the existence of a new class of hereditarily just infinite subgroups of $\Cal J$ which have non-trivial torsion.

21 pages