  A systematic study carried out on the infinite degeneracy and the constants
of motion in the Landau problem establishes the central extension of the
Euclidean group in two dimension as a dynamical symmetry group, and Sp(2,R) as
spectrum generating group irrespective of the choice of the gauge. It may be
noted that the siginificance of the Euclidean group was already implicit in the
earlier works on the Landau problem; in the present paper the method of group
contraction plays an important role. Dirac's remarkable representation of the
group SO(3,2) and the isomorphism of this group with Sp(4,R) are re-visited.
New insights are gained on the meaning of two-oscillator system in Dirac
representation. It is argued that in view of the fact that even the two
dimensional isotropic oscillator having SU(2) as dynamical symmetry group does
not arise in the Landau problem the relevance or applicability of SO(3,2) group
becomes invalid.
