一类仿射型本原非同步置换群的构造  

The Structure about A Type of Affine Primitive Non-synchronizing Groups

作　　者：张志林[1] 杨晋龙 张华[1] 

机构地区：[1]云南师范大学数学学院,云南昆明650500

出　　处：《数学的实践与认识》2016年第18期242-250,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11161058;11561078)

摘　　要：同步置换群的研究是置换群理论中的一个前沿课题.通过在有限域上定义广义Paley图,来讨论这类图的团数(clique number)和色数(chromatic number)相等的条件.然后证明构造的广义Paley图和一类仿射群的轨道图同构,进而讨论这类仿射群的同步性.在此基础上给出一类本原非同步群的构造.The study of synchronizing groups has been the forefront research in the permutation group theory.In this paper we will study the generalized Paley graphs and discuss the condition of the equality between the clique number and chromatic number of the generalized Paley graphs.Then,we will prove that the generalized Paley graphs is isomorphic to the orbital graphs of a certain affine groups,and discuss the synchronization property of a certain affine groups.Furthermore,we will use this property to construct a type of primitive non-synchronizing groups.

关 键 词：同步群 置换群 广义Paley图 

分 类 号：O152.1[理学—数学]