广义四元数群的4-度Cayley图  

4-valent Cayley Graphs of Generalized Quaternion Groups

作　　者：仝允战[1] 袁德有[2] 

机构地区：[1]郑州轻工业学院信息与计算科学系,郑州450002 [2]南阳理工学院应用数学系,南阳473000

出　　处：《数学的实践与认识》2006年第12期269-273,共5页Mathematics in Practice and Theory

摘　　要：一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题.A group G is said to be a generalized quaternion groups, if Q4p = （a,b[a^2n = 1 ,b^2 = a^n,a^b = a^-1）,p ≥3. According to the generalized quaternion group Q4p has only two classes subsets whose numbers of generators are 2, moreover, they are transitive under Aut（Q4p）. Combine the concrete graphs, the method that makes use of to check the circle proved the normality and regularity of 4-Cayley graphs of Q4p about these two subsets of generators. Resolved complete classification problem of 4-valent Cayley graphs.

关 键 词：广义四元数群 CAYLEY图 全自同构群 正规性 正则性 字典式积 

分 类 号：O157.5[理学—数学]