New Properties of a Class of Fuzzy Groups

Being different from Ronsenfield fuzzy groups (RFG) and smooth fuzzy groups (SFG), a class of fuzzy groups (simply FGs) was recently proposed. Homomorphism of FGs had been reported. However, any property of own structure of FGs has not been seen in literature. To solve the problem, this paper puts forward such the definitions as fuzzy fixed elements, fuzzy conjugate class, fuzzy centralizer, fuzzy center, fuzzy p-subgroup, and fuzzy Sylow p-subgroup on the basis of FGs, gives and proves the following theorems: 1. fuzzy Caushy theorem, 2. How many is the number of elements of fuzzy conjugate class, 3.the existence of Fuzzy fixed elements, and 4. fuzzy Sylow theorem. Compared with the previous work of FGs, this paper increases new structural properties for a class of fuzzy groups itself