Non-Solvable Groups whose all Vanishing Class Sizes are Odd-Square-Free

被引：0

作者：

Hafezieh, Roghayeh ^{[1
]}

Conoglu, Gulsemin ^{[1
]}

机构：

[1] Gebze Tech Univ, Dept Math, TR-41400 Gebze, Turkiye

来源：

ADVANCES IN GROUP THEORY AND APPLICATIONS | 2024年 / 19卷

关键词：

conjugacy class; vanishing element; non-solvable group;

D O I：

10.32037/agta-2024-009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a finite group G, a vanishing element is an element x 2 G for which there exists x 2 Irr(G) such that x (x) = 0. The conjugacy class of a vanishing element is called a vanishing class of G. Considering G as a finite non-solvable group with Sol(G) as its solvable radical, in this paper, we prove that if all vanishing class sizes of G are odd-square-free, then either G/Sol(G) is an almost simple group, or it has exactly two chief factors with the properties mentioned in Theorem 1.

引用

页码：77 / 86

页数：10