On fuzzy subgroups of finite Abelian groups

In this paper,we determine the number of fuzzy subgroups of finite abelian group $ G = Z_{p_1}times Z_{p_2} timescdotstimes Z_{p_n},$ where $ p_1,p_2,ldots,p_n $ are all distinct primes. We have used the equivalence relation on the fuzzy subgroups of any group $G$ defined by Sulaiman and Abdul Ghafur cite{GS}in order to determine all fuzzy subgroups of the above mentioned group. We also determined the number of fuzzy subgroups of abelian group $G=Z_{p^n}times Z_q$ under the same equivalence relation.