4p阶二面体群连通3度Cayley有向图的正规性  

On the Normality of Cayley Digraph of Dihedral Group of Order 4p on 3 Degrees Connectivity

作　　者：覃建军 王飞[2] 

机构地区：[1]广西南宁十五中数学组,广西南宁530003 [2]新疆农业大学数理学院,新疆乌鲁木齐830052

出　　处：《数学的实践与认识》2010年第23期177-182,共6页Mathematics in Practice and Theory

摘　　要：设G是一个有限群,S是G的不包含单位元1的非空子集,定义群G关于S的Cayley(有向)图X:=Cay(G,S)如下:V(X)=G,E(X)={(g,sg)|g∈G,s∈S}.Cayley(有向)图X:=Cay(G,S)称为正规的,如果G的右正则表示R(G)在X的自同构群Aut(X)中是正规的.设G是4p阶二面体群(p为素数).考察了Cay(G,S)连通3度的正规性,并给出了这些图的全自同构群.Let G be a finite group and S a subset of G not containing the identity element 1.The Cayley digraph X=Cay（G,S） of G on S is defined by V（X）=G,E（X）={（g,sg）｜g∈G,s∈S}.A Cayley（di）graph X=Cay（G,S） is called normal if right regular representation of G is a normal subgroup of automorphism group of X.Let G is a dihedral group（p for prime numbers）.In This paper we research the normality of Cayley Digraph on 3 degrees of connectivity,and these graph are given the full automorphism group.

关 键 词：二面体群 CAYLEY有向图 正规性 

分 类 号：O157.5[理学—数学]