3p^2阶连通4度Cayley图的正规性  

On the Normality of Connected Tetravalent Cayley Graphs of Order 3p^2

作　　者：徐尚进[1] 郭松涛[1] 王丽[1] 王磊[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西师范大学学报（自然科学版）》2009年第2期30-33,共4页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10161001);广西科学基金资助项目(0832054);广西研究生教育创新计划资助项目(2008105930701M102)

摘　　要：对于一类3p2(p是素数)阶群G=〈a,b,c ap=bp=c3=[a,b]=1,-c 1ac=a-rbr+1,-c 1bc=a,r>1,r3≡1(m od p)〉,研究了其连通4度C ay ley图的正规性,并通过其点稳定子的结构证明G的连通4度C ay ley图均正规。鉴于王艳丽等人的相关工作,这等于圆满解决了3p2阶群的连通4度C ay ley图的正规性问题。For the group G=〈a,b,c｜a^p=b^p=c^3=[a,b]=1,c^-1ac=a^-rb^r＋1, c^-1bc=a,r〉1,r^3≡1（mod p）〉 of order 3p^2（p is a prime）,the normality of its connected tetravalent Cayley graphs is researched in this paper. By determining the structure of their vertex-stabilizer those connected tetravalent Cayley graphs of such group G are proved to be normal. Thus the normality of all connected tetravalent Cayley graphs of order Sp^2,based on the related work by WANG Yan-li,is finally solved.

关 键 词：有限群 正规CAYLEY图 拟本原置换群 

分 类 号：O157[理学—数学]