摘要
为研究有限幂零群G忠实作用在一个可解群H上的轨道长度,假设有限幂零群G忠实不可约作用在一个初等交换q-群V上,则可得Z(G)是循环群,且对任意V中元v,中心化子CG(v)与Z(G)交一定等于1,考虑中心化子阶的情况。假设G是幂零类为2的有限群且Z(G)是循环群,若子群S满足|S|^(2)>|G|,则S与中心Z(G)交不等于1。若G忠实不可约作用在初等交换q-群V上,证明了所有的最小轨道长度的平方大于等于群G的阶。
If a nilpotent group G acts faithfully on a solvable group H,it turned out to be helpful to know the orbit sizes of H in this action.Suppose that a nilpotent group G acts faithfully and irreducibly on V.It is well known that Z(G)is cyclic and the intersection of C_G(v)and Z(G)equals to 1 for any nontrivial element v in V.Let G be a nilpotent group of class 2 with Z(G)cyclic.If S is a subgroup of G with|S|^2>|G|,then the intersection of S and Z(G)is not trival.If G acts faithfully and irreducibly on an elementary abelian N,then the minimal orbit has size large than|G|^(1/2).
作者
薛海波
吕恒
XUE Haibo;LU Heng(School of Mechatronics and Information Engineering,Chongqing College of Humanities,Science and Technology,Hechuan Chongqing 401524;School of Mathematics and Suatistics.Southwest University,Chongqing 400715,China)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
2023年第5期99-102,共4页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金面上项目(No.11971391)。
关键词
有限P-群
轨道
幂零类
finitep-group
orbit
nilpotent class
