关于具有限秩的可解群

On Solvable Groups of Finite Rank

关于具有限秩的可解群本义得到了它的正规列的交换商因子的一种排序，推出了这类群的所有拟循环子群构成它的一个特征子群，证明了秩ｎ的可解群的Ｈｉｒｓｃｈ不变量≤ｎ，并由此界定了秩ｎ的无挠可解群的导出长度．

in this paper, we research the solvable groups of finite rank, and prove that the union set of all quasi-cyclic subgroups of G is a characteristic subgroup and the Hirsch number h(G) does not exceed n if G is a solvable group of rank n. In particular, for an arbitrary solvable torsion-free group G of rank n, we give the upper hound of the derived length of G.