有限群的非交换主因子  

Non-Abelian Chief Factors of Finite Groups

作　　者：鲍宏伟[1] 高百俊 张佳 BAO Hongwei;GAO Baijun;ZHANG Jia(Faculty of Science,Bengbu University,Bengbu 233030,Anhui Province,China;School of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang Uygur Autonomous Region,China;School of Mathematics and Information,China West Normal University,Nanchong 637009,Sichuan Province,China)

机构地区：[1]蚌埠学院理学院,安徽蚌埠233030 [2]伊犁师范大学数学与统计学院,新疆伊宁835000 [3]西华师范大学数学与信息学院,四川南充637009

出　　处：《吉林大学学报（理学版）》2020年第5期1079-1084,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11871058,11501235);教育部春晖计划合作科研项目;安徽省教育厅自然科学基金(批准号:KJ2017A569);西华师范大学基本科研业务费项目(批准号:17E091,18B032).

摘　　要：利用子群的弱M-可补性质讨论有限群非交换主因子的分类,得到如下结果:设H是群G的正规子群,H∈Ep',P是H的Sylow p-子群,其中p是H的奇素因子,如果P的每个极大子群在G中都是弱M-可补的,则H中的每个非交换pd-G-主因子A/B都满足下列条件之一:1)A/B≌PSL(2,7)且p=7;A/B≌PSL(2,11)且p=11;2)A/B PSL(2,2^t)且p=2^t+1>3是Fermat素数;3)A/B≌PSL(n,q),n>2是素数,(n,q-1)=1且p=q^n-1/q-1;4)A/B≌M11且p=11;A/B≌M23且p=23;5)A/B≌Ap且p≥5.从而确定了群的非交换pd-主因子的同构类型.We discuss the classification of non-Abelian chief factors of finite groups by using the weakly M-supplemented property of subgroups and obtain the main results as follows:Let H be a normal subgroup of group G,H∈Ep',and P be a Sylow p-subgroup of H,where p is an odd prime div isor of H.If every maximal subgroup of P is weakly M-supplemented in G,then every non-Abelian pd-G-chief factor A/B below to H satisfies one of the following conditions:1)A/B≌PSL(2,7)and p=7;A/B≌PSL(2,11)and p=11;2)A/B PSL(2,2^t)and p=2^t+1>3 is a Fermat prime;3)A/B≌PSL(n,q),n>2 is a prime,(n,q-1)=1 and p=q^n-1/q-1;4)A/B≌M11 and p=11;A/B≌M23 and p=23;5)A/B≌Ap and p≥5.Thus we determine the isomorphic type of non-Abelian pd-chief factor of a group.

关 键 词：弱M-可补子群 极大子群 极小子群 主因子 

分 类 号：O152.1[理学—数学]