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.
Normal Nuclei and Subnormal Nuclei of Characters
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 ir-reducible 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.
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