有限群的πFΦ-超中心和πFΦ-可补子群  

On πFΦ-hypercentre and πFΦ-supplemented Subgroups of Finite Group

作　　者：张丽[1] 

机构地区：[1]中国科学技术大学数学学院,安徽合肥230026

出　　处：《郑州大学学报（理学版）》2015年第4期1-5,共5页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号11371335

摘　　要：群G的正规子群N称为πFΦ-超中心的(πFΦ-hypercentral),如果N=1或者N≠1且N的每个阶数可被π中某些素数整除的非-Frattini G-主因子是F-中心的.群G的所有πFΦ-超中心子群的积称为G的πFΦ-超中心,并记为ZπFΦ(G).应用πFΦ-超中心定义了πFΦ-可补(πFΦ-supplemented)子群:群G的子群H称为πFΦ-可补的,如果存在G的子群T,使得G=HT且(H∩T)HG/HG≤ZπFΦ(G/HG),其中HG是G的包含在H中的最大的正规子群.研究了πFΦ-超中心的一些性质,并利用πFΦ-可补的概念给出了p-幂零和超可解的几个判断准则.A normal subgroup N of G is called πFΦ-hypercentral in G if N = 1 or N≠1 and every nonFrattini G-chief factor below N with order divided by at least one prime in π,is F-central. The product of all the normal subgroups which are πFΦ-hypercentral in G,is called the πFΦ-hypercentre of G and denoted by Z（ G）. Using the πFΦ-hypercentre of G,the πFΦ-supplemented subgroup was defined： a subgroup H of G was called πFΦ-supplemented in G if there existed a subgroup T of G such that G = HT and（ H∩T） HG/ HG≤ZπFΦ（ G /HG）,where HGwas the largest normal subgroup of G contained in H. The propertie of πFΦ-hypercentre were studied. And obtain some new criterion for p-nilpotency and supersolvability of finite groups were obtained.

关 键 词：SYLOW子群 πFΦ-超中心 πFΦ-可补 P-幂零群 

分 类 号：O152[理学—数学]