B_(π)-特征标的正规分量的原核构造  

The Construction of Nucleus for Normal Constituents of B_(π)-characters

作　　者：晋珺 JIN Jun(Department of Mathematics,Jinzhong University,Jinzhong 030619,China)

机构地区：[1]晋中学院数学系,山西晋中030619

出　　处：《山西大学学报（自然科学版）》2023年第1期119-125,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目(2021L492)。

摘　　要：在π-特征标理论中,Isaacs定义了π-可分群G上不可约特征标的原核并引入了B_(π)-特征标,并给出了在商群G/N为π′-群的条件下,从正规子群N的B_(π)-特征标的原核构造其上方群G的B_(π)-分量的原核的方法。文章在相同条件下,由群G的B_(π)-特征标的原核构造了其在正规子群N的某个不可约分量的原核,作为应用,得到B_(π)-特征标一个基本性质的简化证明。In the π-theory of characters, Isaacs defined a nucleus for each irreducible character, and introduced the B_(π)-character of π-separable groups. If the quotient group G/N is a π’-group, then the nucleus of χ, the irreducible B_(π)-constituent of ψG, can be got by the nucleus of ψ, which is a B_(π)-character of N. In this paper, we prove the nucleus of ψ, a irreducible constituent of χN, can be got by the nucleus of χ, which is a B_(π)-character of G in the situation mentioned above. Our result give a simplified proof of one property of B_(π)-character.

关 键 词：Π-可分群 π-特殊的特征标 π-可分解的特征标 B_(π)-特征标 原核 

分 类 号：O152.6[理学—数学]