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arXiv · 2508.16361

Multiplicities of fields of values of conjugacy classes in finite groups

Juan Martínez Madrid·Marco Vergani
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Abstract

Given a group $G$ we write $h(G)$ to denote the maximum number of times that a field extension of $\mathbb{Q}$ appears as the field of values of a conjugacy class of a group. In this work, we prove that $|G|$ is bounded in terms of $h(G)$. Moreover, we classify the groups with $h(G)\leq 3$.

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Juan Martínez Madrid, Marco Vergani. 2025-08-22. Multiplicities of fields of values of conjugacy classes in finite groups. https://arxiv.org/abs/2508.16361

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