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

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-10-25 DOI:10.1090/tran/8926

Nguyen Hung

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引用次数: 0

Abstract

Let p p be a prime and G G a finite group. We propose a strong bound for the number of p ′ p’ -degree irreducible characters of G G in terms of the commutator factor group of a Sylow p p -subgroup of G 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 p -rationality level of p ′ 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 p=2 .

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有限群的𝑝-rationality的连续性和𝑝′度特征的下界

设p p是素数，G G是有限群。利用G G的Sylow p p -子群的换易子因子群，给出了G G的p ' p '次不可约字符个数的一个强界。这个界是由Navarro和Tiep[论坛数学]最近的一个猜想产生的。Pi 9 (2021)， pp. 1-28]在字符值领域和p ' p '度字符的p ' p '理性水平的连续性现象上的研究。这种连续性特性反过来又由著名的McKay-Navarro猜想(见G. Navarro [Ann。的数学。(2) 160 (2004)， pp. 1129-1140)。我们得到了p=2的界和连续性。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.