On Orbits of the Ring Z_n~m under Action of the Group SL(m, Z_n)

摘要

We consider the action of the finite matrix group SL(m,Z_n) on the ring Z_n~m. We determine orbits of this action for n arbitrary natural number. It is a generalization of the task which was studied by A. A. Kirillov for m=2 and n prime number.