Group Gamma(2) and the fractional quantum Hall effect

We analyze the action of the inhomogeneous modular group Gamma (2) on the three cusps of its principal fundamental domain in the Poincare half plane. From this, we obtain an exhaustive classification of the fractional quantum Hall numbers. This classification, in which the integer and the fractional states appear on an equal level, is somehow similar to the one given by Jain. We also present some resulting remarks concerning direct phase transitions between the different quantum Hall states.