摘要
设群G是有限群.如果对G的任意循环子群A,都存在素数p,使得|G∶N_G(A)||p,那么称G为NP-群.利用循环群的自同构群的性质和群作用等处理手段,证明了有限NP-群G是亚交换群,进而改进了目前已有的关于NP-群已经取得的结论,即有限NP-群G的导长至多是3.
A finite group Gis called a NP-group if there is a prime number psuch that｜G∶N_G（A）｜｜pfor every non-normal cyclic subgroup Aof G.In this paper,by using the property of autormorphism group of cyclic group and group action,it proves that a finite NP-group Gis meta-abelian and improved the result that a derived length of a finite NP-group Gis at most 3.
作者
薛海波
蹇祥
吕恒
XUE Hai-bo;JIAN Xiang;LU Heng(Department of Science and Engineering,Chongqing College of Humanities Science and Technology,Hechuan Chongqing 401524,China;School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
2018年第8期6-9,共4页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11471266)
中央高校基本科研业务专项基金项目(XDJK2015B033)
