广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (5): 160-167.doi: 10.16088/j.issn.1001-6600.2022020703

• 综述 • 上一篇    下一篇

有限群不可约特征标的余次数

卢家宽*, 王宇, 张博儒, 庞琳娜   

  1. 广西师范大学 数学与统计学院, 广西 桂林 541006
  • 收稿日期:2022-02-07 修回日期:2022-03-22 出版日期:2022-09-25 发布日期:2022-10-18
  • 通讯作者: 卢家宽(1980—), 男(壮族), 广西贵港人, 广西师范大学教授, 博士。E-mail: jklu@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11861015, 12161010); 广西自然科学基金(2020GXNSFAA238045)

Codegrees of Irreducible Characters in Finite Groups

LU Jiakuan*, WANG Yu, ZHANG Boru, PANG Linna   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2022-02-07 Revised:2022-03-22 Online:2022-09-25 Published:2022-10-18

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摘要： 设G是有限群,χ∈Irr(G),称cod(χ)=|G∶ker χ|χ(1)为不可约特征标χ的余次数。该算术量最近10多年被越来越多的学者关注,从多方面开展研究,取得不少成果。本文从余次数的算术条件对有限群结构的影响、余次数与其他算术量之间的联系等方面综述该领域的相关研究成果,同时,列举一些尚未解决的问题,供读者参考。

关键词: 不可约特征标, 余次数, 可解群, p-长, Huppert猜想

Abstract: Let G be a finite group, and χ∈Irr(G). The number cod(χ)=|G∶ker χ|χ(1) is called the codegree of the character χ. This paper makes a review on the results concerning codegree of irreducible character in finite groups in particular, lists some problems which are still open.

Key words: irreducible character, codegree, solvable groups, p-length, Huppert’s conjecture

中图分类号: 

  • O152.1
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