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  • Author: Helge Glöckner x
  • General Mathematics x
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Abstract

Let G be a totally disconnected, locally compact group admitting a contractive automorphism α. We prove a Jordan-Hölder theorem for series of α-stable closed subgroups of G, classify all possible composition factors and deduce consequences for the structure of G.

Abstract

We show that every finite-dimensional p-adic Lie group of class Ck (where k ∈ ℕ ∪ {∞}) admits a Ck-compatible analytic Lie group structure. We also construct an exponential map for every k + 1 times strictly differentiable (SC k+1) ultrametric p-adic Banach-Lie group, which is an SC 1-diffeomorphism and admits Taylor expansions of all finite orders ≤ k.