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 the dihedral group of order 2ⁿ with a cyclic group of order 2.

finite p-groups, nilpotent group, fuzzy subgroups, dihedral group, Inclusion-Exclusion Principle, maximal subgroups.