Structure of Solvable Subgroups in SL(n,C) and Its Application to Fuchsian System

It is given a structure of solvable subgroup which has finite element in this paper.The solvable group of SL(n,C) and the solvability of Fuchsian equation are contracted by Khovanskiy theorem,such that the solvability of Fuchsian equation' research is transformed the solvability of its monodromy group' research.On the basis of the structure theorem of solvable group in SL(n,C),we will discuss the structure of solvable group in SL(n,C),and we will apply it to the study of the integrability of Fuchsian equation.