摘要
首先对Sylow p-子群为循环群的6p^(n)阶非交换群G的结构进行了分类,其中p>5,为素数.当p≡1(mod 3)时,G≌G_(1),G_(2),G_(3),G_(4),G_(5);当p 1(mod 3)时,G≌G_(2),G_(4),G_(5).接着讨论了这类群的非交换图,即对此类有限非单群采用了非交换图刻画,利用图论和群论的基本知识计算得到Sylow p-子群循环的6p^(n)阶非交换群的结构与其非交换图之间具有一一对应关系,即这五类群的非交换图互不同构,进一步发展了A.Abdollahi等提出的猜想2.
First,this paper classifies the structure of non-abelian groups G of order 6p^(n)(where p>5 is a prime)whose Sylow p-subgroups are cyclic.Specifically,when p≡1(mod3),G≌G_(1),G_(2),G_(3),G_(4),G_(5);when p 1(mod3),G≌G_(2),G_(4),G_(5).Then,it discusses the non-abelian graphs of such groups,i.e.,using non-abelian graphs to characterize these finite non-simple groups.By calculating with the basic knowledge of graph theory and group theory,it is concluded that there is a one-to-one correspondence between the structure of non-abelian groups of order 6p^(n)with cyclic Sylow subgroups and their non-abelian graphs.In other words,the non-abelian graphs of these five types of groups are non-isomorphic to each other,which further develops Conjecture 2 proposed by A.Abdollahi et al.
作者
王蓉
雒晓良
WANG Rong;LUO Xiaoliang(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong,Shanxi 030619,China)
出处
《平顶山学院学报》
2025年第5期11-14,共4页
Journal of Pingdingshan University
基金
山西省教育厅科技创新项目(2020L0518)。
关键词
非交换图
中心化子
度数
同构
non-commutative graph
centralized
degrees
isomorphism
