共轭可置换子群对群结构的影响  

Influence of Conjugate-permutable Subgroups on Structure of Finite Groups

作　　者：钟祥贵[1] 郭静安[1] 单俊辉[1] 张福生[1] 

机构地区：[1]广西师范大学数学科学学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2008年第1期38-41,共4页Journal of Guangxi Normal University:Natural Science Edition

基　　金：广西科学基金资助项目(0575050;0640061);广西研究生教育创新计划资助项目(2007106020701M51)

摘　　要：利用Sylow子群完备集中元素的共轭可置换子群获得了有限群为幂零或超可解的几个等价条件和若干充分条件,并刻画了合数阶循环子群均共轭可置换和非共轭可置换子群均共轭的有限群。Using conjugate-permutable subgroups in a complete set of Sylow subgroups of a group,some equivalent and sufficient conditions for a group to be nilpotent or supersolvable are obtained, those groups whose cyclic subgroups with composite number order are all conjugate-permutable or whose nonconjugate-permutable subgroups are all conjugated.

关 键 词：共轭可置换子群 极小非幂零群 幂零群 超可解群 

分 类 号：O152.1[理学—数学]