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

Hung, Nguyen

doi:10.1090/tran/8926

The continuity of $p$-rationality and a lower bound for $p’$-degree characters of finite groups
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by Nguyen Ngoc Hung;

Trans. Amer. Math. Soc. 377 (2024), 323-344

DOI: https://doi.org/10.1090/tran/8926

Published electronically: October 25, 2023

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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 [Forum Math. Pi 9 (2021), pp. 1–28] 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 (see G. Navarro [Ann. of Math. (2) 160 (2004), pp. 1129–1140]). We achieve both the bound and the continuity property for $p=2$.

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