Zeros of Monomial Brauer Characters
Zeros of Monomial Brauer Characters
复制标题
单项式布劳尔特征的零点
DOI：
10.1007/s11401-019-0127-7
复制
发表时间：
2019
影响因子：
0.5
通讯作者：
Chen Gang
中科院分区：
文献类型：
--
作者：
Chen Xiaoyou;Chen Gang
设一个有限群和一个固定素数。如果gis的Ap-Brauer特征是由g的某个子群（不一定是固有群）的线性- brauer特征导出的，则称其为单项式特征。用IBrm(G)表示G的不可约单- brauer字符集。LetH=G ' op ' (G)是使G/His为阿别良群的最小正规子群。设G∈Gis为正则元素，因子群pg / hg的阶数不除|IBrm(G)|。则存在φ∈IBrm(G)使得φ(G) = 0。
LetGbe a finite group andpbe a fixed prime. Ap-Brauer character ofGis said to be monomial if it is induced from a linearp-Brauer character of some subgroup (not necessarily proper) ofG. Denote by IBrm(G) the set of irreducible monomialp-Brauer characters ofG. LetH=G′Op′(G) be the smallest normal subgroup such thatG/His an abelianp′-group. Suppose thatg∈Gis ap-regular element and the order ofgHin the factor groupG/Hdoes not divide |IBrm(G)|. Then there existsφ∈ IBrm(G) such thatφ(g) = 0.