关于莫利秩3的无限群结构的探讨  

Study on the Structures of the Connected Groups of Morley Rank 3

作　　者：杨年西[1] 

机构地区：[1]淮北师范大学信息学院,安徽淮北235000

出　　处：《长春师范大学学报》2017年第6期12-14,共3页Journal of Changchun Normal University

基　　金：安徽高校自然科学研究重点资助项目"模型论在群论中的应用研究"(KJ2016A646)

摘　　要：为了研究莫利秩3的连通群的结构,将其分成两类,分别是好群和坏群。本文在已知有限莫利秩的无限群具有降链条件下,利用降链条件,证明了坏群G是莫利秩3的连通群且Z(G)=1,则x≠1,x∈G,C_G(x)是连通的莫利秩1的群。x,y≠1,x,y∈G,群C_G(x)和群C_G(y)在群G中相互共轭或相等。We considered two classes of connected groups of Morley rank 3 is conducive to the study of its structure, respectively they are a good group or bad group. We know that any infinite group of finite Morley rank satisfies the descending chain condition, according to the descending chain condition, we show that G be a centerless, bad group of connected groups of Morley rank 3, Then x ≠1,x ∈ G, CG （x） be a connected groups of Morley rank 1 ,and x,y≠l ,x,y∈ G,CG（x）and CG（y） are conjugate to each other or equal.

关 键 词：可解群 有限莫利秩群 连通群 无限群 

分 类 号：O142[理学—数学]