Some model theory of profinite groups

  • Tim Clausen

    Universität Münster, Germany
  • Katrin Tent

    Universität Münster, Germany
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The main purpose of these notes is to give more background and details for the results obtained in [13] which rely heavily on deep results by Lazard, Lubotzky, Mann, du Sautoy and others. At the center is Lazard's purely group theoretic characterization of -adic analytic groups given in [8] (see Section 4.2 below). By Lazard's result a compact topological group is a -adic analytic group if and only if it has an open uniformly powerful pro- subgroup (see Section 3).