Mathematics
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Item 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.Item The explict formula for the number of the distinct fuzzy subgroups of the cartesian product of the dihedral group 2n with a cyclic group of order eight, where n>3(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 8, where n>3.Item Classifying fuzzy subgroups of certain dihedral group D2p5(2019) Olayiwola, A.; EniOluwafe, M.In this paper, we give an explicit formula for counting the number of distinct fuzzy sub-groups of dihedral group D2ps for any prime(p) and any integer s≥1. This we achieved using the algorithm described on the most recent equivalence relation ≈ known in the literature to classify fuzzy groups.Item New equivalence relation for the classification of fuzzy subgroups of symmetric S4(2018-01) Ogiugo, M. E.; EniOluwafe, M.In this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is studied. Without any equivalence relation on fuzzy subgroups of group G, the number of fuzzy subgroups is infinite, even for the trivial group. The number of distinct fuzzy subgroups with respect to the new equivalence relation is obtained for S4.Item Classifying a class of the fuzzy subgroups of the alternating groups A(n)(2017) Ogiugo, M. E.; EniOluwafe, M.The aim of this paper is to classify the fuzzy subgroups of the alternating group. First, an equivalence relation on *the set of all fuzzy subgroups of a group G is defined. Without any equivalence relation on fuzzy subgroups of group G, the number of fuzzy subgroups is infinite, even for the trivial group. Explicit formulae for the number of distinct fuzzy subgroup of finite alternating group are obtained in the particular case n = 5. Some inequalities satisfied by this number are also established for n≥ 5.