On The Unitriangular Group Of Order6Over The Integral Ring

Let Tr1(n,Z) be the group of all upper unitriangular matrices over the integral ring. Let ky(1≤i<j≤n)be given nonzero integers andAchievements have been made when kij and do not have to zero, the unit triangular matrix group Tr1,(n,Z) subgroup structure; well as some kij=0when, n=3and n=4when the unit triangular matrix group Tr1(n,Z) subgroup structure. This article will discuss the structure of the upper triangular matrix subgroup of order six units of the whole group on the ring. Including G is Tr1(6,Z) subgroup conditions; flocks when G,The first chapter introduces the research background and significance, research, involving relevant knowledge to.The second chapter gives a G is Tr1(6,Z) subgroup conditions; flocks when G, It’s the center of the case group column. Entire process can be divided into two categories, The first category k12,k23,k34,k45,k56Only in the case of a zero second largest category of k13,k24,k35,k46Only in the case of a zero.Finally, we summarize the work done in this paper, and proposed further study of the issue.