A counterexample to a conjecture of A. R. Miller

Let $χ$ be an irreducible character of a finite group $G$. A. R. Miller conjectured that the proportion of elements $g\in G$ such that $χ(g)$ 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.

Publication Details

Journal
ArXiv.org
Published
2025-10-12
Primary Topic
Finite Group Theory Research
Type
article
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article

A counterexample to a conjecture of A. R. Miller

ArXiv.org
Finite Group Theory Research
article

A counterexample to a conjecture of A. R. Miller

article en

Abstract

Let $χ$ be an irreducible character of a finite group $G$. A. R. Miller conjectured that the proportion of elements $g\in G$ such that $χ(g)$ 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.

ArXiv.org
Openalex Percentile: Top 36%
Finite Group Theory Research
Open Access PDFOpenAlex
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A counterexample to a conjecture of A. R. Miller · ArXiv.org (2025) | TGRS Research Map | TGRS