In this paper, the explicit formulae is given for the number of distinct fuzzy subgroups of the cartesian product of the dihedral group of order 2n with a cyclic group of order eight, where n > 3.
The problem of classification of fuzzy subgroups can be extended from finite p-groups to finite nilpotent groups. Accordingly, any finite nilpotent group can be uniquely written as a direct product of p-groups. In this paper, we give explicit formulae for the number of distinct fuzzy subgroups of the Cartesian product of two abelian groups of orders 2n−1 and 4 respectively for every integer n >2.
