关于莫利秩2的连通群的性质探讨

Study on Properties of the Connected Groups of Morley Rank 2

有限莫利秩的无限群类似于在代数闭域上的线性代数群,已知有限莫利秩的无限群具有降链条件,利用降链条件,证明莫利秩2的连通的非可解群包含两个连通的莫利秩1的交换群且两子群交是1;通过对2个群的乘积的莫利秩计算,证明莫利秩2的连通群是可解群.

An infinite group of finite Morley rank is analogous to a linear algebraic group in an algebraicallyclosed field.It is known that any infinite group of finite Morley rank satisfies the descending chain condition.According to the descending chain condition,a nonsolvable connected group of Morley rank 2 contains twoconnected commutative subgroups of Morley rank 1,and their intersection is 1. By calculating Morley rank ofthe product of two groups,it is proved that a connected group of Morley rank 2 is solvable.