有限群的最大子群的性质对群结构的影响(英文)  

The Influence of the Properties of Maximal Subgroups on the Structure of a Finite Group

作　　者：李样明[1] 王燕鸣[2] 

机构地区：[1]广东教育学院数学系,广州广东510310 [2]中山大学岭南学院数学与计算科学学院,广州广东510275

出　　处：《数学进展》2007年第5期599-606,共8页Advances in Mathematics（China）

基　　金：This work was supported in part by NSFC(No.10571181);NSF of Guangdong(No.06023728);ARF(GDEI).

摘　　要：有限群G的一个子群称为在G中是π-拟正规的若它与G的每一个Sylow-子群是交换的.G的一个子群H称为在G中是c-可补的若存在G的子群N使得G=HN且H∩N≤HG=CoreG（H）.本文证明了：设F是一个包含超可解群系U的饱和群系,G有一个正规子群H使得G/H∈F.则G∈F若下列之一成立：（1）H的每个Sylow子群的所有极大子群在G中或者是π-拟正规的或者是c-可补的;（2）F^＊（H）的每个SyloW子群的所有极大子群在G中或者是π-拟正规的或者是c-可补的,其中F^＊（H）是H的广义Fitting子群.此结论统一了一些最近的结果.A subgroup of a finite group G is called π--quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup N of G such that G = HN and H M N ≤ HG = Corec （H）. In this paper we prove： Let F- be a saturated formation containing U, the class of all supersolvable groups and suppose that G is a group with a normal subgroup H such that G/H∈F . Then G∈F if one of following holds： （1） All maximal subgroups of all Sylow subgroups of H are either π-quasinormal or c-supplemented in G; （2） All maximal subgroups of all Sylow subgroups of F^＊ （H）, the generalized Fitting subgroup of H, are either π--quasinormal or c- supplemented in G. These unify some recent results.

关 键 词：Π-拟正规子群 C-可补子群 超可解群 广义FITTING子群 群系 

分 类 号：O152.1[理学—数学]