弱φ-可补子群对有限群结构的新刻画  

The new characterization of weakly φ-supplemented subgroups on the structure of finite groups

作　　者：赵勇[1] ZHAO Yong(School of Education,Guang′an Vacational and Technical College,Guang′an 638000,China)

机构地区：[1]广安职业技术学院师范学院,四川广安638000

出　　处：《高师理科学刊》2022年第5期12-15,共4页Journal of Science of Teachers＇College and University

摘　　要：设F是子群闭的局部群系,G是可解的有限群.通过群系理论,利用极小子群的弱φ-可补性,证明了G∈δ的充要条件是存在G的正规子群E,使得G/E∈δ,并且p∩Gδ的所有p阶子群及4阶循环子群均在G中弱φ-可补,其中p是|G|的满足(|G|,p-1)=1的素因数.利用该结论,得到了一系列推论,丰富和推广了相关结果.Let F be local formation with closed subgroups,G be a finite solvable group,based on the theory of the class of groups and the weakly φ-supplemented of minimal subgroup,it was proved that G∈δ if and only if G has a normal subgroup E such that G/E∈δ and the subgroups of order p or 4 of Ep∩Gδ are weakly φ-supplemented in G,where p is the prime factor of G satisfied by(|G|,p-1)=1.By the result above,a series of corollaries was obtained,which enrich and generalize the related results.

关 键 词：局部群系 有限群 弱φ-可补子群 δ-剩余类 

分 类 号：O152.1[理学—数学]