I'm confused: at the beginning it is given that "Let's assume that G has a normal sub-group of order 3 and let a be her generator ( <a>=G ).", but this is absurd: I think they meant a is the generator of the normal sbgp. of order 3, not of G.
Also, in (2), whatever the conditions are, it can't be , since has no normal sbgp. of order 3, as given at the beginning...check this and write back with al the conditions clearluy stated.