= R-analytic pro-p group
{c}
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.
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