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.
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
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)
关键词
有限群
正规CAYLEY图
拟本原置换群
finite group
normal Cayley graph
quasiprimitive permutation groups
