scholarly works
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Item The Fuzzy Subgroups for the Nilpotent (P-Group) of (D23 × C2m) for M ≥ 3(2022) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.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 23 with a cyclic group of order of an m power of two for, which m ≥ 3.Item On the Nilpotent Fuzzy Subgroups of the Abelian Type: Z32 × Z2n , n ≥ 5(2020) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.The 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.Item FUZZY SUBGROUPS FOR (THE CARTESIAN PRODUCT OF) THE ABELIAN STRUCTURE : Z16×Z2n, n > 3(2020) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.As part of the extension of the finite nilpotent groups to the direct product of p-groups, we give in this paper, the explicit formulae for the number of distinct fuzzy subgroups of the abelian structure given by: ℤ16 × 2, n > 3, the Cartesian product of two abelian groups of orders 2n and 16 respectively for every integer n > 3Item On the p-Groups of the Algebraic Structure of D2n × C8(2020) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.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.Item The Modular Group of the form : M2n x C2(International Journal of Fuzzy Mathematical Archive, 2020) Adebisi, S. A.; EniOluwafe, M.In this paper, the classification of finite -groups is extended to the group of the modular structure x , and the number of distinct subgroups were computed, making the classification of the given structure possible for the given prime = 2Item The Generalized Quarternion p-Group of Order 2n : Discovering the Fuzzy Subgroups(International Journal of Fuzzy Mathematical Archive, 2020) Adebisi, S.A.; EniOluwafe, M.In this paper, the classification of finite p-groups is extended to the cartesian product of the generalized quarternion group of order 2n with a cyclic group of order 2 which also belongs to the class of the famous nilpotent groupsItem The fuzzy subgroups for the abelian structure Z8 x Z2n , n > 2(Nigerian Mathematical Society, 2020) Adebisi, S. A.; Ogiugo, M.; EniOluwafe, M.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 and 8 respectively for every integer n > 2 .Item An explicit formula 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(Pushpa Publishing House, Prayagraj, India, 2020) Adebisi, S. A.; EniOluwafe, M.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.Item Determining the number of distinct fuzzy subgroups for the abelian structure Z4 x Z2n-1 ,n > 2(2020) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.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.Item Computing the number of distinct fuzzy subgroups for the nilpotent p-group of D2n x C4.(2020-03) Adebisi, S. A.; Ogiugo, M.; EniOluwafe, M.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 four, where n > 3.