The fuzzy subgroups for the nilpotent ( p-group) of (d۲۳ × c۲m) for m ≥ ۳

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 ۲۳ with a cyclic group of order of an m power of two for, which m ≥ ۳.

Keywords:

finite p-groups , nilpotent group , Fuzzy subgroups , Dihedral group , Inclusion-Exclusion Principle , maximal subgroups