CHARACTERIZATION OF P-ADIC ANALYTIC GROUPS IN TERMS OF WREATH-PRODUCTS

We show that a finitely generated pro-p group is p-adic analytic (i.e., can be given the structure of a Lie group over Qp) if and only if it does not involve arbitrarily large wreath products of the form Cp wr Cp. This result, whose proof applies Zelmanov's recent solution to the restricted Burnside problem, is in fact equivalent to Zelmanov's Theorem. © 1992.