Characteristic Fuzzy subgroups and Abelian Fuzzy subgroups
DOI:
https://doi.org/10.65405/4rsymv96Keywords:
Characteristic Fuzzy subgroups, abelian Fuzzy subgroups, normal fuzzy subgroup, G-fuzzy subgroupAbstract
In this paper we present some basic concepts of fuzzy set theory. With properties of normal fuzzy subgroups. Fuzzy analogs of some group theoretic concepts such as cosets, conjugate fuzzy subgroups, quotient groups. The order of fuzzy subgroup. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroups. We prove that if µ is a fuzzy subgroup of a group G such that the fuzzy index of µ is the smallest prime dividing the order of G, then µ is a normal fuzzy subgroup.
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