On an equivalence of fuzzy subgroups I

This paper forms a sequel to the paper "On an Equivalence of Fuzzy Subgroups I". Here we determine the number of distinct equivalence classes of fuzzy subgroups of G = Z p 1 + ... + Z p n where p 1 , p 2 ,...., p n are distinct primes. We introduce the notion of a keychain of a chain of length n + 1 and index of a keychain in order to determine the number of fuzzy subgroups of G . We achieve this by using induction on the index of a keychain.