Elena Black (1998) showed that D_n (the dihedral group of order 2n) for n odd satisfies the arithmetic lifting property. We shall discuss what additional conditions are needed to show that D_n has the arithmetic lifting property for arbitrary n, and will show that these conditions are satisfied in certain special cases. To present the arithmetic lifting property in context, we will also speak of the Noether Problem and some examples (Maeda's answer for A_5) and 'counterexamples'.