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arXiv · 2510.10734

A counterexample to a conjecture of A. R. Miller

Gabriel Navarro·Benjamin Sambale
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Abstract

Let $\chi$ be an irreducible character of a finite group $G$. A. R. Miller conjectured that the proportion of elements $g\in G$ such that $\chi(g)$ is zero or a root of unity is at least 1/2. We construct a character of a perfect group of order 69120 such that this proportion is 511/1152.

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Gabriel Navarro, Benjamin Sambale. 2025-10-12. A counterexample to a conjecture of A. R. Miller. https://arxiv.org/abs/2510.10734

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