On Orbits of the Ring Zmn under Action of the Group SL(m, Zn)

Abstract

We consider the action of the finite matrix group SL(m,Zn ) on the ring Zmn. 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.

Keywords

• ring
• finite group