Artin’s theorem

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 42)

Abstract

Let G be a finite group and let x1, ..., x h be its distinct irreducible characters. A class function on G is a character if and only if it is a linear combination of the x i ’s with non-negative integer coefficients. We will denote by R+ (G) the set of these functions, and by R(G) the group generated by R+(G), i.e., the set of differences of two characters. We have
$$ R\left( G \right) = {Z_{x1}} \oplus \cdots \oplus Z{x_h}. $$

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Chaire d’algèbre et géométrieCollège de FranceParisFrance

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