关于完全C＊置换子群  

On Completely C＊-Permutable Subgroups of Finite Groups

作　　者：李世荣[1] 卢家宽[1] 刘伟[1] 孟伟[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《大学数学》2009年第1期20-24,共5页College Mathematics

基　　金：广西自然科学基金资助项目(0249001)

摘　　要：设H≤G,称H为G的完全C*置换子群,如果对G的任意素数幂阶子群K,恒有x∈〈H,K〉,使得HKx=KxH.本文利用素数幂阶子群的完全C*置换性给出了一个群属于给定群系的的若干充要条件.A subgroup H of G is called completely C＂ -permutable in G provided for every subgroup K of prime power order of G there exits an element x∈（H, K） such that HKx = KxH. In this paper, by using the completely C＊ -permutability of subgroups of prime power order. Some sufficient and necessary conditions which inply a finite group to belong to a given formation will be obtained.

关 键 词：完全C＊置换子群 饱和群系 P-幂零群 超可解群 

分 类 号：O152.1[理学—数学]