Abstract
The concepts of internal direct product and external direct product of fuzzy subgroups of a group ℷ are established as well as that of fuzzy isomorphism of fuzzy subgroups (of possibly different groups). It is shown that the internal direct product of two fuzzy subgroups of a group ℷ is isomorphic to their external direct product. The fuzzy counterparts of the first and third isomorphism theorems are also proved.
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