Mathematics
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Item A VECTOR MATRIX APPROACH OF COUNTING CYCLIC QUOTIENTS OF SOME ABELIAN P-GROUPS(2009) Enioluwafe, M.We determine in this paper, the precise number of cyclic quotients of Abelian p-groups of exponent p i and rank r > 1, i = 1, 2, . . . , n for all natural numbers nItem The Subgroups for the Finite p-Group of the Structure D24 x C25(2022) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.Every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. Efforts are carefully being intensified to calculate, in this paper, the explicit formulae for the number of distinct fuzzy subgroups of the cartesian product of the dihedral group of order with a cyclic group of order of an m power of two for, which .Item The Computation for the Fuzzy Subgroups of the Algebraic Structure D2> x C-z(2022) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.Any finite uilpoleut group can be uniquely written as a direct product of /<- groups In this paper, an attempt for the compulation of Dv.i x CTi was made. This happens to be the eomputatioii of the number of distinct fuzzy subgroups of the cartesian product of the dihedral group of order 24 with a cyclic group of order sixteenItem The Number of Chains of Subgroups in the Lattice of Subgroups of Group(2022) Ogiugo, M.; Seghal, A.; Adebisi S.A.; EniOluwafe, M.In this paper, we established the number of chains of subgroups in the subgroup lattice of the Cartesian product of the alternating group and cyclic group using computational technique induced by the set of representatives of isomorphism classes of subgroupsItem 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 The Modular Nilpotent Group Mpn × Cp for p > 2(2021) Adebisi, S. A.; EniOluwafe, M.In this paper, the classification of finite p-groups is extended to the modular nilpotent group of the form Mpn × Cp in which, p is greater than 2Item The Number of Chains of Subgroups of the Group Zm ×Sn,n ≤ 5,m ≤ 3(2021) Ogiugo, M.; Adebisi, S.A.; EniOluwafe, M.The study of chains of subgroups in this paper describes the set of all chains of subgroups of G that end in G which is used to solve many computational problems in fuzzy group theory. It is also showed that a fuzzy subgroup is simply a chain of subgroups in the lattice of subgroups.Item The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups(Science Publishing Group, 2021) Adebisi, S.A.; Ogiugo, M.; EniOluwafe, M.In the recent past, results have shown that Nilpotent groups such as p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the number of distinct fuzzy subgroups of various finite p-groups including those of square-free order. However, not much work has been done on the fuzzy subgroup classification for the nilpotent groups formed from the Cartesian products of p-groups through their computations. Here, part of our intention is therefore trying to make some designs so as to classify the nilpotent groups formed from the Cartesian products of p-groups through their computations. The Cartesian products of p-groups were taken to obtain nilpotent groups. Results up to two dimensions are now obtainable. In this paper, the fuzzy subgroups of the nilpotent product of two abelian subgroups of orders 2n and 128. The integers n ≥ 7 have been successfully considered and the derivation for the explicit formulae for its number distinct fuzzy subgroups were calculated. Some methods were once being used in counting the chains of fuzzy subgroups of an arbitrary finite p-group G. Here, the adoption of the famous Inclusion-Exclusion principle is very necessary and imperative so as to obtain a reasonable, and as much as possible accurateItem 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 > 3