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 J . In particular, we establish a new approach to evaluating commutators in J and using this method investigate the normal subgroup structure of some classes of index subgroups of J as introduced by Klopsch. We provide new proofs of Fesenko's results that lead to a proof that the torsion free group T={t+∑ k⩾1a kt qk+1: a k∈ 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 J which have non-trivial torsion.
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