Profinite Groups

  • Luis Ribes
  • Pavel Zalesskii
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 40)


Let C be a nonempty class of finite groups [this will always mean that C contains all the isomorphic images of the groups in C]. Define a pro — C group G as an inverse limit
$$G = \mathop {\underleftarrow {\lim }}\limits_{i \in I} {G_i}$$
of a surjective inverse system {G i, φij I} of groups G i in C, where each group G i is assumed to have the discrete topology. We think of such a pro — C group G as a topological group, whose topology is inherited from the product topology on П i∈I G i.


Normal Subgroup Finite Group Galois Group Closed Subgroup Fundamental System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Luis Ribes
    • 1
  • Pavel Zalesskii
    • 2
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Department of MathematicsUniversity of BrasiliaBrasiliaBrazil

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