On Fundamental Algebraic Characterizations of μ-Fuzzy Normal Subgroups - Ibtisam Masmali; Umer Shuaib; Abdul Razaq; Areeba Fatima; Ghaliah Alhamzi (Journal of Function Spaces)
In this article, we present the study of μ-fuzzy subgroups and prove numerous fundamental algebraic attributes of this newly defined notion. We also define the concept of μ-fuzzy normal subgroup and investigate many vital algebraic characteristics of these phenomena. In addition, we characterize the quotient group induced by this particular fuzzy normal subgroup and establish a group isomorphism between the quotient groups G/κμ and G/κ∗μ. Furthermore, we initiate the study of level subgroup, open level subgroup, and tangible subgroup of a μ-fuzzy subgroup and emphasize the significance of μ-fuzzy normal subgroups by establishing a relationship between these newly defined notions and μ-fuzzy normal subgroup.