THE LARGEST CHARACTER DEGREES OF THE SYMMETRIC AND ALTERNATING GROUPS

被引：5

作者：

Halasi, Zoltan ^{[1
]}

Hannusch, Carolin ^{[1
]}

Hung Ngoc Nguyen ^{[2
]}

机构：

[1] Univ Debrecen, Inst Math, Dept Algebra & Number Theory, Pf 12, H-4010 Debrecen, Hungary

[2] Univ Akron, Dept Math, Akron, OH 44325 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 05期

关键词：

Symmetric groups; alternating groups; character degrees; largest character; ORDER;

D O I：

10.1090/proc/12920

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the largest character degree of an alternating group An with n >= 5 can be bounded in terms of smaller degrees in the sense that b(A(n))(2) < Sigma(psi is an element of Irr(An)) (psi(1)<b(An)) psi(1)(2) where Irr(A(n)) and b(A(n)) respectively denote the set of irreducible complex characters of A(n) and the largest degree of a character in Irr(A(n)). This confirms a prediction of I. M. Isaacs for the alternating groups and answers a question of M. Larsen, G. Malle, and P. H. Tiep.

引用

页码：1947 / 1960

页数：14

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