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user 91692
For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.
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Equality of subsets of abelian groups
$\DeclareMathOperator\Irr{Irr}$You can see this from the fact that for abelian groups, irreducible characters form a $\mathbb{C}$-basis of the space of functions from $G$ to $\mathbb{C}$. … Hence, both $J(A)$ and $[A,A]$ are trivial, and the above theorem says that the common zero set of irreducible complex characters is trivial. …
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