有限群的Sylow-子群的弱s-可补极大子群(英文)  

On Weakly s-supplemented Maximal Subgroups of Sylow Subgroups of Finite Groups

作　　者：李样明[1] 

机构地区：[1]广东第二师范学院数学系,广州广东510310

出　　处：《数学进展》2011年第4期413-420,共8页Advances in Mathematics（China）

基　　金：supported in part by NSFC(No.10871210);NSF of Guangdong(No.06023728)

摘　　要：假设G是一个有限群，H是G的一个子群．称H在G是s-置换的，若对G的任意的Sylow-子群Gp，有HGp=GpG；称H在G是弱s-可补的，若存在G的子群T使得G=HT且HnT≤HsG，其中Hsc是所有包含在H中的G的s-置换子群生成的子群．本文给出了下列定理：设厂是一个包含超可解群系“的饱和群系，有限群G有一个正规子群H使得G／H∈F．若F^＊（H）的每个Sylow子群的所有极大子群在G中是弱s-可补的，其中F^＊（H）是H的广义Fitting子群，则G∈F．它是J，Algebra，2007,315：192-209一文中的Skiba公开问题在极大子群情形下的肯定回答．Suppose G is a finite group and H is subgroup of G. H is said to be s-permutable in G if HGp =GpH for any Sylow p-subgroup GB of G; H is called weakly s-supplemented subgroup of G if there is a subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. In this paper, the following theorem was given： Let F be a saturated formation containing U, the class of all supersolvable groups and G be a group with E as a normal subgroup of G such that G/H ∈F Suppose that every maximal subgroup of Sylow subgroups of F^＊（H） is weakly s-supplemented in G. Then G ∈F. It is a positive answer for Skiba＇s open questions in J. Alqebra, 2007, 315：192-209 in the maximal subgroup case.

关 键 词：弱s-可补子群 超可解 饱和群系 广义FITTING子群 

分 类 号：O152.1[理学—数学]