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

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.