THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP

被引：29

作者：

Isaacs, I. M. ^{[1
]}

Loukaki, Maria ^{[2
]}

Moreto, Alexander ^{[3
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ Crete, Dept Math, GR-7140 Iraklion, Greece

[3] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2013年 / 197卷 / 01期

关键词：

Finite Group; Conjugacy Class; Maximal Subgroup; Abelian Subgroup; Solvable Radical;

D O I：

10.1007/s11856-013-0013-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a finite group G, we write acd(G) to denote the average of the degrees of the irreducible characters of G. We show that if acd(G) <= 3, then G is solvable. Also, if acd(G) < 3/2, then G is supersolvable, and if acd(G) < 4/3, then G is nilpotent.

引用

页码：55 / 67

页数：13

共 7 条

[1]

[Anonymous], 1967, ENDLICHE GRUPPEN

[2]

Ernest John A., 1961, Trans. Amer. Math. Soc., V99, P499, DOI DOI 10.2307/1993559

[3] NUMBER CONJUGACY CLASSES IN FINITE GROUP [J].