On the average character degree and the average class size in finite groups

被引：21

作者：

Qian, Guohua ^{[1
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Jiangsu, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2015年 / 423卷

关键词：

Finite group; Character degree; Class size; MINIMAL DEGREES; PROBABILITY;

D O I：

10.1016/j.jalgebra.2014.11.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let acd(G) and acs(G) denote the average irreducible character degree and the average conjugacy class size, respectively, of a finite group G. The main objective of this paper is to find the lower bounds of acd(G) and acs(G) for a non-r-solvable group G where r is a prime. We show that PSL(2, r), where r >= 5, is a non-r-solvable group with the smallest average character degree and the smallest average class size. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1191 / 1212

页数：22

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