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Fuzzy cosets in AG-groups
AIMS Mathematics 2022, 7(3): 3321-3344
Published: 15 March 2021
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In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if A is any fuzzy AG-subgroup of G, then μ A ( x y ) = μ A ( y x ) for all x , y G, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number [ G : A ]. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange's theorem of finite AG-group is also introduced.

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