有限群不可约特征标的余次数

Codegrees of Irreducible Characters in Finite Groups

设G是有限群,χ∈Irr(G),称cod(χ)=|G∶kerχ|/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。

Let G be a finite group,andχ∈Irr(G).The number cod(χ)=|G∶kerχ|/χ(1)is called the codegree of the characterχ.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.