Rasul Rasuli - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.
Mohammad Mehde Moatamedi nezhad - University of Applied Science and Technology, Tehran, Iran.
Hossien Naraghi - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.

In this paper, using a t-norm T, we define and introduce the notions fuzzysubgroups, direct product of fuzzy subgroups, normal fuzzy subgroups andnormal direct product of fuzzy subgroups. Next we investigate theirproperties and obtain some new results about them. Later, we investigatethem under group homomorphisms.

fuzzy groups, t-norm,direct products.