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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. Itis a generalization of the task which was studied by A.A. Kirillov for $m=2$and $n$ prime number.

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