Khalid Abdul-Aziz Holayan Al-Shammari2022-05-182022-05-185062https://drepo.sdl.edu.sa/handle/20.500.14154/2146In this thesis we introduce the annuli of a fuzzy subgroup and use it as a tool to give alternate proofs of some properties of fuzzy subgroups and to straighten out some known results on fuzzy normal and fuzzy abelian groups and obtain some new results about them. It is also used to describe the left and right fuzzy cosets determined by a fuzzy subgroup. We obtain some commutative diagrams which relate to homomorphisms, fuzzy subgroups and fuzzy quotient groups. Finally, we straighten out some chains of fuzzy normal subgroups which lead to the concept of fuzzy solvable groups.enThesis