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LSpice
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equality Equality of subsets of abelian groups

Let G$G$ be a finite abelian group, X$X$ and Y$Y$ be two non-empty subsets of G$G$ of equal size. Suppose that for each irreducible character $\chi$ of G$G$ we have $\sum_{x\in X}\chi(x)=\sum_{y\in Y}\chi(y)$. Is thisit true that $X=Y$ in general?

equality of subsets of abelian groups

Let G be a finite abelian group, X and Y be two non-empty subsets of G of equal size. Suppose that for each irreducible character $\chi$ of G we have $\sum_{x\in X}\chi(x)=\sum_{y\in Y}\chi(y)$. Is this true that $X=Y$ in general?

Equality of subsets of abelian groups

Let $G$ be a finite abelian group, $X$ and $Y$ be two non-empty subsets of $G$ of equal size. Suppose that for each irreducible character $\chi$ of $G$ we have $\sum_{x\in X}\chi(x)=\sum_{y\in Y}\chi(y)$. Is it true that $X=Y$ in general?

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user53093
user53093
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equality of subsets of abelian groups

Let G be a finite abelian group, X and Y be two non-empty subsets of G of equal size. Suppose that for each irreducible character $\chi$ of G we have $\sum_{x\in X}\chi(x)=\sum_{y\in Y}\chi(y)$. Is this true that $X=Y$ in general?