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Squares of characters and finite groups

Edith Adan-Bante
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Abstract

Let $G$ be a group of odd order and $χ$ be a complex irreducible character. Then there exists a unique character $χ^{(2)}\in\Irr(G)$ such that $[χ^2,χ^{(2)}]$ is odd. Also, there exists a unique character $ψ\in \Irr(G)$ such that $[ψ^2, χ]$ is odd.

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Edith Adan-Bante. 2005-08-02. Squares of characters and finite groups. https://arxiv.org/abs/math/0410582

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