On The Unitriangular Group Of Order5Over The Integral Ring

Let Tr1,(n,Z) be the group of all upper unitriangular matrices over the integral ring. Let kij(1≤i<j≤n)be given nonzero integers andThis paper continues to study n=5, subgroup structure of triangular group of units. Including G is Tr1,(5,Z)be subgroup conditions;when the G groups, the Situation about the upper central series and the lower central series of the group G,and contact conditions both the upper central series and the lower central series of the group G.In the first chapter, we introduced some of this paper is to use the basic concepts. Then, for this article involves the problem background, progress and results give a simple review.In the second chapter, we have expanded the main part of this paper, through the special method to get the G groups from the general, upper and lower center of the group out. And study its upper and lower center column group overlap conditions.Finally, we have this paper summarizes the work done by, and put forward further research problems.