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Some Applications of Groups

  • Igor R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 11)

Abstract

Galois theory studies the’ symmetries’, that is, the automorphisms of finite extensions; see § 6 for the definition of finite extensions and their simplest properties. For simplicity, we will assume that the fields under consideration are of characteristic 0, although in fact all the main results hold in much greater generality, for example, also for finite fields.

Keywords

Normal Subgroup Irreducible Representation Galois Group Fundamental Theorem Galois Theory 
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 2005

Authors and Affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of ScienceMoscowRussia

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