 Center of an Iwasawa algebra of a complete p-valued group (source code)

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= Center of an Iwasawa algebra of a complete p-valued group
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If $G$ is a complete finite-rank p-valued group with center $Z(G)$, then
$$
Z\bigl(\mathbb F_p[[G]]\bigr)=\mathbb F_p[[Z(G)]].
$$
The key facts are that the finite-conjugacy center of a p-valued group equals its center and that compatibility through the finite group-algebra quotients eliminates coefficients on infinite conjugacy classes.

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