= Uniform pro-p group and powerful Lie lattice correspondence
The <Lie algebra of a uniform pro-p group> construction and <BCH convergence on a powerful Lie lattice> are mutually inverse on objects and morphisms. On the group side morphisms are continuous <group homomorphisms>; on the lattice side they are linear <Lie algebra homomorphisms> over the <p-adic integers>. A group homomorphism respects powers, roots and limits, and a Lie homomorphism respects every convergent <Baker--Campbell--Hausdorff formula> term.
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