**Abstract: **
The aim of the talk is to determine the number of elements of
the finite nonabelian matrix group SL(m,Z_n). We will define
the group action on the ring (Z_n)^m and find the corresponding
orbits. Furthermore, we will discuss the group action of
SL(2,Z_n) on (Z_n)^2 x (Z_n)^2 together with the orbits.