direct product of ifmsn (g)

In this paper we introduced direct product of intuitionistic fuzzy multigroups of g under norms(ifmsn(g)) and we prove that it will be also ifmsn(g). next we shall study some important properties and theorems for them. on the other hand we shall give the definition of the identity element, strong upper- lower and weak upper- lowerof them and study the main theorem for this. we shall also give new results on this subject. also we define the concepts of conjugate and commutative of ifmsn(g) and investigate them under direct product. finally, we organize them under group homomorphisms and we prove that the image and preimage of direct product of ifmsn(g) will be also ifmsn(g).