Abstract
We investigate the inner structure of fuzzy subgroups with sup property. We provide a characterization of this type of fuzzy subgroups in terms of their level subsets. It is shown that the property of being a fuzzy subgroup with sup property is invariant under homomorphism and the homomorphic preimage of a fuzzy subgroup with sup property is also a fuzzy subgroup with sup property. Moreover, we investigate the lattice structure of the class L n t of fuzzy normal subgroups of a group G, each of which assumes the same value “ t” at the identity of G. It is proved that the subclass L ns t of fuzzy subgroups with sup property of L n t constitutes a sublattice of L n t . The modularity of L ns t is derived as a consequence of the modularity of L n t .
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