The continuity of p-rationality and a lower bound for p'-degree characters of finite groups

2022/05/31 by Hung Ngoc Nguyen, Hung, Nguyen N. · 1 citation
Computer Science · Engineering · Mathematics · #20C15 #20C33 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2205.15899

openalex publication_date 2022/05/31 · openalex created_date 2023/02/14 · openalex updated_date 2026/07/28

Abstract

Let p be a prime and G a finite group. We propose a strong bound for the number of p'-degree irreducible characters of G in terms of the commutator factor group of a Sylow p-subgroup of G. The bound arises from a recent conjecture of Navarro and Tiep [NT21] on fields of character values and a phenomenon called the continuity of p-rationality level of p'-degree characters. This continuity property in turn is predicted by the celebrated McKay-Navarro conjecture [Nav04]. We achieve both the bound and the continuity property for p=2.

Cited by

• The Isaacs--Navarro Galois conjecture

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• On almost p-rational characters of p'-degree
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• On the number of p'-degree characters in a finite group
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