Adebisi, S.A.Ogiugo, M.EniOluwafe, M.2025-05-152020https://repository.ui.edu.ng/handle/123456789/10609The extension of the finite nilpotent groups is now being diversified. As such, results up to two dimensions are now obtainable. In this paper, the fuzzy subgroups of the nilpo tent abelian structure given by: Z32 × Z2n , the cartesian product of two abelian subgroups of orders 2n and 32 respec tively for every integer n > 5 have been carefully studied and the explicit formulae for its number distinctly given.enFinite p-GroupsAbelian GroupFuzzy subgroupsisomorphicInclusion-Exclusion PrincipleMaximal subgroupsNilpotent groupExplicit formulaeArticle