Abstract
We prove a number of results about fuzzy groups involving the concepts of fuzzy cosets and fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer, and Abelian groups. We prove that if μ is a fuzzy subgroup of a group G such that the fuzzy index of μ is the smallest prime dividing the order of G, then μ is a fuzzy normal subgroup. Also, we show that there is a one-to-one correspondence between the fuzzy (right) cosets of a fuzzy subgroup μ of a group G and the (right) cosets of a certain subgroup H of G.
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