Sylow-子群的自同构导子是小的有限群  

Finite Groups with Small Automizers for Their Sylow Subgroups

作　　者：卢家宽 孟伟[2] 王静静 LU Jia kuan;MENG Wei;WANG Jing jing(School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi 541004,China;School of Mathematics and Computer Science,Yunnan Minzu University,Kunming,Yunnan 650031,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004 [2]云南民族大学数学与计算机科学学院,云南昆明650031

出　　处：《河北北方学院学报（自然科学版）》2017年第5期17-19,共3页Journal of Hebei North University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11461007;11361075);广西自然科学基金面上项目(2016GXNSFAA380156);广西高校数学与统计模型重点实验室开放课题(2016GXKLMS002)

摘　　要：目的研究自同构导子对有限群结构的影响。方法使用单群分类定理及圈积等手段,分可解群、非可解群两种情况分别讨论。结果证明了Sylow子群的自同构导子是小的有限群恰是幂零群。结论某些特殊子群的自同构导子对有限群的结构具有很强的影响,对自同构导子附加合适条件后,可以得到有限群若干信息。ObjectiveTo investigate the influence of Automizer on the structure of finite groups.MethodsBy the classification of finite simple groups and wreath product,the groups are divided into solvable and non solvable groups.ResultsIt proves that finite groups with small automizers for their Sylow subgroups are nilpotent groups.ConclusionThe automizers of some subgroups have a strong influence on the structure of finite groups.Adding suitable conditions to automizers can lead to certain information of finite groups.

关 键 词：自同构导子 幂零群 可解群 

分 类 号：O152.1[理学—数学]