Fuzzy C-Normal Subgroups And Fuzzy Weakly C-Normal Subgroups Of Finite Groups

In this paper,several special definition of fuzzy subgroups,such as fuzzy maximalnormal subgroup,fuzzy minimal subgroup,fuzzy minimal normal subgroup, etc,areproposed.However,the main work is around the fuzzy c-normal subgroups and fuzzyweakly c-normal subgroups.The main contents may be summarized as follows:1. Firstly,the fuzzy c-normal subgroups and fuzzy weakly c-normal subgroupswere defined,and their properties were studied,including the homomorphism,isomorphism,etc.2. Secondly,the relationship between the fuzzy c-normal subgroups and fuzzyweakly c-normal subgroups were explored,some sufficient conditions fromfuzzy weakly c-normality to fuzzy c-normality were obtained.3. Finally, several necessary and sufficient conditions of solvablity and nilpotecywere obtained by using fuzzy weakly c-normality to fuzzy c-normality ofsome special fuzzy subgroups of finite groups.Moreover,some sufficientconditions of solvable groups were given.