  Two dimensional inversion symmetry ($180^{\circ}$ rotations in the ``Hall
plane'' that hosts the incompressible electron fluid that exhibits the
quantized Hall effect) is identified as its fundamental unbroken symmetry. A
consequence is that the integers $p$ and $q$ which define both the Landau level
filling factor $\nu$ = $p/q$ and the elementary fractional charge $\pm e/q$ of
topological excitations, cannot have a common divisor greater than 2.
