Huppert可裂性定理的一个推广  

A Generalization of Huppert's Splitting Theorem

作　　者：贾婷婷[1] 郝成功[1] JIA Ting-ting HAO Cheng-gong(School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Chin)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《中北大学学报（自然科学版）》2017年第1期27-30,共4页Journal of North University of China(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(201601D011006)

摘　　要：研究了一个有限群何时在某个正规子群上可裂的问题,推广了著名的Huppert可裂性定理,主要把Huppert可裂性定理中讨论的p-版本推广到π-版本并对其进行了详细的证明,从而得到一个更为广泛的证明可裂性的判据.其证明引用了经典的Gaschütz可裂性定理,运用了传输同态,采用了由特殊到一般的证明思路.最后,作为对该定理的实际应用,给出了若干经典的传输定理的统一的简化证明.The problem concerning when a finite group is splitting over a normal subgroup is studied and the famous Huppert＇s splitting theorem of p-version is generalized to n-version. A detailed proof is supplied and a broader splitting criterion is obtained. The proof used the classical Gaschutz theorem and the transfer homomorphism. The main idea of the proof is from special to general. Finally, as applications of the theorem, unified and simplified proofs of some classical theorems in the theory of transfer are given.

关 键 词：可裂性 正规子群 矿商群 交换矿商群 

分 类 号：O152.1[理学—数学]