 R-analytic pro-p group

For a pro-p ring $R$, an $R$-analytic pro-p group is a pro-p group equipped with an analytic manifold structure locally modelled on open subsets of a finite free $R$-module, such that multiplication and inversion are given locally by convergent power series. The number of local coordinates is its analytic dimension. The Nottingham group admits no such structure over any pro-$p$ ring: its hereditary just infiniteness, unbounded finite cyclic torsion and sub-base-three derived-series growth exclude both alternatives in the analytic just-infinite structure theorem.