关于Berger定理的推广  

On a Generalization of Berger’s Theorem

作　　者：常慧敏 黄宇敏 CHANG Huimin;HUANG Yumin(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）》2022年第4期954-959,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12101374);山西省青年基金(20210302124077);山西省高等学校科技创新项目(2020L0041)。

摘　　要：Berger定理断言任意可解群G中的拟本原复特征标也是本原的,文章考察了该定理关于正规子群L?G的相对情形。为了统一研究复特征标和Brauer特征标的本原性和拟本原性的关系,引入了L-本原的和L-拟本原的π-部分特征标,证明了在适当的可解性条件下L-拟本原性等价于L本原性,该结果加强并推广了Berger定理。Berger’s theorem asserts that quasi-primitive complex characters of any solvable group G are also primitive.The relative version of this theorem with respect to a normal subgroup L?G was studied.In order to simultaneously investigate the relationship between primitivity and quasi-primitivity of complex characters and of Brauer characters,L-primitive and L-quasi-primitiveπ-partial characters were introduced.It was proved that L-quasi-primitivity and L-primitivity are equivalent under a suitable solvability condition,which strengthens and generalizes Berger’theorem.

关 键 词：可分群 本原特征标 拟本原特征标 π-部分特征标 BRAUER特征标 

分 类 号：O152[理学—数学]