有关C-可补子群  

On the C-supplement Subgroups

作　　者：赵勇[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《广西科学》2007年第1期6-10,共5页Guangxi Sciences

基　　金：四川省学位委员会资助;四川省教育厅重点学科建设基金项目资助。

摘　　要：运用群系理论讨论Sylow子群的极大子群和Sylow子群的二次极大子群,以及极小子群对有限群结构的影响.得到(1)设G是与A4无关的有限群,P是G的最小素因数,F是包含Np的群系,则G∈F的充要条件为G存在一个正规子群,使得G/H∈F且H的Sylowp-子群的二次极大子群在G中C-可补;(2)设F是非空子群闭的局部群系,G是有限群,p是G的最小素因数且GF是可解,那么G∈FG存在正规子群N使得G/N∈F且对于P∈Sylp(N),P∩GF的22阶循环子群在G中C-可补且极小子群皆包含在ZF∞(G)中.The C -supplement condition on the maximal subgroup or the second maximal subgroup of Sylow subgroup and the minimal subgroup of G are used to study the structure of G by the theory of formations. The following results are obtained. （1）Let G be a finite group which is A4 -free and F- be a formation containing Np ,where p is the smallest prime number dividing ｜ G｜. Then G ∈F, and there exists a normal subgroup H of G such that G/H∈F and the second maximal subgroup of Sylow p- subgroup of H is C- supplement in G. （2）Let F be non-empty and subgroup-closed formation, G be a finite group and G^F is solvable. Then G∈F,and there exists a normal subgroup N of G such that G/N∈F, and for p ∈ Sylp （G）, the subgroups of prime order and the subgroup of order 4 are contained in Z∞^F（G）. The result above generalizes some known ones.

关 键 词：群系 有限群 C-可补 

分 类 号：O152[理学—数学]