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The Artin Symbol, Reciprocity Law, and Class Field Theory

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 110)

Abstract

Let K/k be an abelian extension, and let p be a prime of k which is unramified in K. We had seen in Chapter I, §5 that there exists a unique element σ of the Galois group (G, lying in the decomposition group GP (for any P|p, they all coincide in the abelian case) having the effect
$$\sigma \alpha \equiv \alpha ^{\text{Np}} (\bmod \,\,\,\text{P}),\quad \quad \quad \quad \quad \quad \quad \quad \alpha \in o_k .$$

Keywords

Prime Number Galois Group Finite Index Class Field Open Subgroup 
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 New York Inc. 1986

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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