(untitled) (International Journal of Environmental Sciences, 2025)
In this paper our main focus is to give the lattice structure ????????(????) of the lattice of subgroups of the groups of the upper triangular matrices of the 2×2 matrices over ???????? under matrix multiplication modulo ????, where ???? is prime. The lattice structure ????????(????) is displayed for ????=2,3,5 and 7.The subgroups are singled out by means of Lagrange’s theorem, Sylow’s theorem, a result of N.BourBaki etc.