特征标的正规原核与次正规原核  

Normal Nuclei and Subnormal Nuclei of Characters

作　　者：王蕾[1] WANG Lei(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2024年第1期134-139,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(20210302123429)。

摘　　要：对于一个给定的不可约复特征标,一般而言它的正规原核和次正规原核是不相同的,研究它们何时重合是一个很基本的问题。2001年,Isaacs和Navarro利用Hall子群的拟本原特征标构造了一类不可约复特征标。本文将证明这类特征标的正规原核和次正规原核是相同的,从而加强了Isaacs和Navarro的结论,并给出了若干应用。In general,normal nuclei and subnormal nuclei are different for a given irreducible complex character,and it is a basic problem to study that when these two classes of nuclei coincide with each other.In 2001,Isaacs and Navarro introduced a class of irreducible complex characters that are induced from qusi-primitive characters of Hall subgroups.In this paper,we show that normal nuclei of these characters are the same as subnormal nuclei.This strengthens Isaacs and Navarro's result and several applications are given.

关 键 词：Π-可分群 正规原核 次正规原核 B_(π)-特征标 N_(π)-特征标 

分 类 号：O152[理学—数学]