The fuzzy subgroups for the nilpotent ( p-group) of (d23 × c2m) for m ≥ 3

A group is nilpotent if it has a normal series of a finite length n. By this notion, every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. 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 2^3 with a cyclic group of order of an m power of two for, which m ≥ 3.