= Brauer induction
{c}
{title2=$\chi=\sum_j n_j\operatorname{Ind}_{H_j}^G\lambda_j$}
Every complex <character of a representation> of a <finite group> $G$ is an integer linear combination of <characters> of <induced representations> from one-dimensional <group representations> of subgroups $H_j\leq G$. 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 $s=1$ to abelian extensions.
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