Every complex character of a representation of a finite group is an integer linear combination of characters of induced representations from one-dimensional group representations of subgroups . Negative coefficients are allowed. Unlike Artin induction, the subgroups need not be cyclic groups. Applied to an Artin L-function, compatibility with induced representations turns this character identity into a product of one-dimensional Artin L-functions with integer exponents, reducing the behavior at to abelian extensions.
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