The Total Character of a Finite Group

被引：2

作者：

Humphries, Stephen ^{[1
]}

Kennedy, Chelsea ^{[1
]}

Rode, Emma ^{[1
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

来源：

ALGEBRA COLLOQUIUM | 2015年 / 22卷

关键词：

symmetric group; dicyclic group; Murnaghan-Nakayama rule; Chebyshev polynomial;

D O I：

10.1142/S100538671500067X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The total character tau(G) of a finite group G is the sum of the irreducible characters of G. We present conditions under which tau(G) can be written as a polynomial with integer coefficients in an irreducible character of G. Such a group we call a total character group. We show that the dicyclic group of order 4n is a total character group if and only if n equivalent to 2,3 mod 4. The polynomial used is a sum of Chebyshev polynomials of the second kind. We also show that S-n (n >= 4) is not a total character group.

引用

页码：775 / 788

页数：14

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