We provide some characterizations of completely prime (completely semiprime) and 3-prime (3-semiprime) N-groups. The relationship between a 3-prime (completely prime) N-ideal P of an N-group I" and the ideal (P: I") of the near-ring N is investigated. Moreover, the notion of IFP N-ideal is defined. We prove that the concept of IFP N-ideal occurs naturally where N is a left permutable (left self distributive, subcommutative) near-ring and I" a monogenic N-group. Also, we obtain some relationships between an IFP N-ideal P of an N-group I" and the ideal (P: I") of the near-ring N.