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Profinite Groups

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

Abstract

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.

Keywords

Normal Subgroup Finite Group Galois Group Closed Subgroup Fundamental System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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