子群的M-可补性对群结构的影响  

The influence of M-supplementation of subgroups on the structure of finite groups

作　　者：王娜儿[1] 顾春华[2] 

机构地区：[1]浙江海洋学院数理与信息学院,浙江舟山316000 [2]江阴职业技术学院基础部,江苏江阴214433

出　　处：《扬州大学学报（自然科学版）》2010年第3期13-16,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10901133)

摘　　要：若存在子群K使得G=HK,且对于H的任意极大子群H1,有H1K为G的真子群,则称子群H在G中是M-可补的.利用M-可补子群的性质对p-幂零群结构进行研究,得到一些新结果:①设G是有限群,p是|G|的奇素因子,P∈Sylp(G),则G是p-幂零群当且仅当P在G中M-可补,且NG(P)是p-幂零群.②设G是有限群,p是|G|的奇素因子,P∈Sylp(G).若P的任意极大子群在G中M-可补,且NG(P)是p-幂零群,则G是p-幂零群.A subgroup H is called M-supplemented in a finite group G,if there exists a subgroup K of G such that G=HK and H1K is a proper subgroup of G for any maximal subgroup H1 of H.By considering the M-supplemented primary subgroups,this paper get some new results on the structure of p-nilpotent groups： ① Let p be an odd prime divisor of ｜G｜ and P∈Sylp（G）.Then G is p-nilpotent if and only if P is M-supplemented in G and NG（P） is p-nilpotent.② Let p be an odd prime divisor of ｜G｜ and P∈Sylp（G）.If every maximal subgroup of P is M-supplemented in G and NG（P） is p-nilpotent,then G is p-nilpotent.

关 键 词：有限群 M-可补 P-幂零群 准素子群 

分 类 号：O152.1[理学—数学]