| The main topic of this dissertation is application of Lie-theoretic techniques to questions of finite presentability of pro-p groups. We settle the last open case of a conjecture concerning finite presentability of open pro-p subgroups of connected, simply-connected simple algebraic groups over nonarchimedean local fields. We also establish finite presentability of the Nottingham group NFp (the group of wild automorphisms of the local field Fp ((t))) for p > 2, thus giving a positive answer to the question of the existence of a finitely presented pro- p group which contains an isomorphic copy of every finitely generated pro-p group. The proof of finite presentability of NFp is based on the study of a previously unknown family of its subgroups. These groups can be thought of as non-linear deformations of SL12F pt and have other interesting properties. In the last chapter we investigate other aspects of the subgroup structure of the Nottingham group NFp . In particular, we show that finitely generated subgroups of NFp of positive Hausdorff dimension cannot be linear over a local field. This result has several applications to the problem of classification of just-infinite pro-p groups of finite width. |
