Abstract
In this paper, we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups. Moreover, we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups. We also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups. Also, we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image.
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