  We show that there is a kind of quantum group symmetry $ sl_{q}(2) $ in the
usual Landau problem and it is this quantum group symmetry that governs the
degeneracy of Landau levels. We find that under the periodic boundary
condition, the degree of degeneracy of Landau levels is finite, and it just
equals the dimension of the irreducible cyclic representation of the quantum
group $ sl_{q}(2) $.
