  The complete set of ground state wave functions for N anyons in an external
magnetic field on the torus is found. The cases when the filling factor is less
than or equal to one are considered. The single valued description of anyons is
employed through out by coupling bosons to a Chern-Simons field. At the end,
the Chern-Simons interaction is removed by a singular gauge transformation as a
result of which the wave functions become multi-component in agreement with
other studies.
