Abstract
As interest in pro-p Groupss has grown, so has interest in the Nottingham group. Known to number theorists as the group of wild automorphisms of the local field\( \mathcal{N} = \mathcal{N}({\mathbb{F}_q})\) (where q = p e ), this finitely generated pro-p Groups.\( \mathcal{N} = \mathcal{N}({\mathbb{F}_q})\) was introduced to the group theory community in the work of D. Johnson [13] (himself inspired by an article of S. Jennings [12]) and his Ph.D. student I. York [26] [27]. Viewing S as a group of formal power series under substitution, D. Johnson and I. York proved many of the initial structural results. Some of the proofs are reproduced below and the reader will see the ease with which one can calculate within the group. This, alongside the group’s interesting properties, has led to the Nottingham group becoming a favourite test case for conjectures concerning pro-p Groupss.
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Camina, R. (2000). The Nottingham Group. In: du Sautoy, M., Segal, D., Shalev, A. (eds) New Horizons in pro-p Groups. Progress in Mathematics, vol 184. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1380-2_6
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