Abstract
Two dimensional inversion symmetry (180^∘ 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 ν = p/q and the elementary fractional charge ± e/q of topological excitations, cannot have a common divisor greater than 2.