有限群的子群弱补  

Weakly-complemented Subgroups of Finite Groups

作　　者：苏跃斌[1] 

机构地区：[1]四川理工学院理学院,四川自贡643000

出　　处：《四川理工学院学报（自然科学版）》2009年第1期9-10,共2页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：利用有限群的某些子群弱补性给出了一个群是F热-群的一个充分条件。设F=LF(f)是一个子群闭的局部群系,满足每个极小非F-群是可解的,N G,G/N∈F若N的每个p阶子群含于Zf∞(G),且4阶循环群在G中弱补,则G∈F。A sufficient condition of F-group is given by using weakly-complemented of some subgroups for a finite group. Let F = LF（f） be a subgroup-closed local formation such that minial non- F- groupa is solvable. It is proved that： if there exists a normal subgroups N of G such that G/N E Fand every cyclic subgroups of N of order 4 is weakly-complemented in G and every element of N of prime order is contained in Z^f= （G） ,then G is a Fgroup.

关 键 词：弱补子群 F-群 局部群系 可解群 

分 类 号：O152.1[理学—数学]