Higher order states in the multiple series fractional quantum Hall effect.

We report results on the fractional quantum Hall effect in GaAs/Al(x)Ga (1-x)As heterostructures at fractional Landau level filling factor nu=p/q obtained with the combination of a dilution refrigerator and the National Magnet Laboratory hybrid magnet. We establish conclusively the precise quantization of the higher order states p in the series q.