完全条件置换子群对有限群结构的影响  

Influence of completely conditionally permutable subgroups on the structure of finite groups

作　　者：陶司兴[1,2] 薛瑞雪[3] 郭秀云[3] 

机构地区：[1]商丘师范学院数学系,河南商丘476000 [2]上海大学理学院,上海200444 [3]信阳师范学院计算机与信息技术学院,河南信阳464000

出　　处：《苏州大学学报（自然科学版）》2009年第3期5-8,共4页Journal of Soochow University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10471085)

摘　　要：有限群G的子群H称为G的完全条件置换子群,如果对于G的任一子群K,存在x∈〈H,K〉,使得HKx=KxH.文中利用完全条件置换子群对有限群结构的影响,给出了超可解群的若干充分条件,并将一些结果进行了推广.A subgroup H of a finite group G is said to be completely conditionally permutable in G if for every subgroup K of G,there exists an element x ∈ 〈H,K〉 such that HK^z=K^zH. Some sufficient conditions for a group to be supersoluble are obtained by using the influence of completely conditionally permutable subgroups on the structure of finite groups, and some results are generalized.

关 键 词：完全条件置换子群 群系 超可解群 

分 类 号：O152.1[理学—数学]