Multiplicities of fields of values of conjugacy classes in finite groups

2025/08/22 by Madrid, Juan Martínez, Vergani, Marco
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.16361

Abstract

Given a group G we write h(G) to denote the maximum number of times that a field extension of 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)≤ 3.

Citations

• Uniformly semi-rational simple groups
• On groups with at most five irrational conjugacy classes
• More on Landau's theorem and Conjugacy Classes
• Groups with small multiplicities of fields of values of irreducible characters

Related

• Multiplicities of conjugacy class sizes of finite groups
• Groups with small multiplicities of fields of values of irreducible characters
• Finite groups have even more conjugacy classes
• A lower bound for the number of conjugacy classes of finite groups
• Finite extension of group with infinite conjugacy classes