On the Largest Character Degree and Solvable Subgroups of Finite Groups

被引：0

作者：

Wu, Zongshu ^{[1
]}

Yang, Yong ^{[2
]}

机构：

[1] Stanford Online High Sch, Redwood City, CA 94063 USA

[2] Texas State Univ, Dept Math, San Marcos, TX 78666 USA

来源：

RESULTS IN MATHEMATICS | 2025年 / 80卷 / 03期

关键词：

D O I：

10.1007/s00025-025-02401-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a finite group, and pi be a set of primes. The pi-core O-pi(G) is the unique maximal normal pi-subgroup of G, and b(G) is the largest irreducible character degree of G. In 2017, Qian and Yang proved that if H is a solvable pi-subgroup of G, then |HO pi(G)/O-pi(G)|<= b(G)(3). In this paper, we improve the exponent of 3 to 3log(504)(168)<2.471. Along the way, we also prove that if a solvable group P acts faithfully on X, then there is some 3-coloring of X such that there are no more than root|P| elements of P that preserve the coloring.

引用

页数：12

共 12 条

[1]

Breuer T., 2024, The GAP Character Table Library-a GAP package, 1.3.9

[2] Large orbits in coprime actions of solvable groups [J].