| 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Sylow p-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∈F⇔G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Z∞F(G)中. |
| 关键词: 群系 有限群 C-可补 |
| DOI： |
| 投稿时间：2006-06-20修订日期：2006-09-19 |
| 基金项目:四川省学位委员会和四川省敬育厅重点学科建设基金项目资助。 |
|
| On the C-supplement Subgroups |
|
ZHAO Yong
|
| (College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, China) |
| Abstract: |
| 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. (l) Let G be a finite group which is A4-free and G 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/N∈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 GF 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. |
| Key words: formations finite groups C-supplement |
