scholarly works
Permanent URI for this collectionhttps://repository.ui.edu.ng/handle/123456789/410
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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.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 Combinatorics of counting distinct fuzzy subgroups of certain dihedral group(2019) Olayiwola, A.; EniOluwafe, M.This paper is devoted to counting distinct fuzzy subgroups (DFS) of finite dihedral group D2n, where n is a product of finite number of distinct primes, with respect to the equivalence relation ≈ . This counting has connections with familiar integer sequence called ordered Bell numbers. Furthermore, a recurrence relation and generating function was derived for counting DFS of D2n.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 Counting subgroup formula for the groups formed by cartesian Product of the generalized quaternion group with cyclic group of order two("National Mathematical Centre, Abuja & Department of Mathematics, University of Ibadan, Ibadan, NIGERIA", 2015) EniOluwafe, M.The main goal of this note is to determine an explicit formula of finite group formed by taking the Cartesian product of the generalized quaternion group of two power order with a order two cyclic groupItem Counting subgroups of finite non-metacyclic 2-groups having no elementary abelian subgroup of order(2014-10) EniOluwafe, M.The aim of this note is to give an explicit formula for the number of subgroups of finite nonmetacyclic 2-groups having no elementary abelian subgroup of order 8.Item Counting subgroups of nonmetacyclic groups of type: D2(n-1) x C2 , n ≥ 3(2015) EniOluwafe, M.The main goal of this note is to determine an explicit formula of finite group formed by taking the Cartesian product of the dihedral group of two power order with a order two cyclic groupItem 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 Exhibition of normal distribution in finite p-groups(Scientific & Academic Publishing, 2017) Adebisi, A. S.; EniOluwafe, M.Suppose that G is a group of order m p and n ≤ m. Let Sn(G) be the number of subgroups of order p n in G. Then, the number of subgroups of order pn is normally distributed with respect to n, where n is a positive integer.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 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 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 G-theory of group rings for groups of elementary abelian p-groups(2009) EniOluwafe, M.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 On counting subgroups for a class of finite nonabelian p-groups and related problems(2017) Olapade, O. O.; EniOluwafe, M.The main goal of this article is to review the work of Marius Tarnauceanu, where an explicit formula for the number of subgroups of finite nonabelian p-groups having a cyclic maximal subgroups was given. Using examples to clarify our work and in addition we give an explicit formula to some related problems.Item On the extension problem and the nil groups of rings of finite global dimension(2013) Olusa, O. S.; Ilori, S. A.; EniOluwafe, M.Vanishing result is obtained in respect of nil groups of rings of finite global dimension. Also a connection is established with the extension problem.Item On the number of cyclic quotients of some abelian p-groups(2007-11) EniOluwafe, M.We determine in this paper, the precise number of cyclic quotients of Abelian p-groups of exponent p and rank r > 1; / = 1 and 2Item On the precise order of unit groups of burnside rings of some finite abelian group(2008-05) EniOluwafe, M.We determine the precise order of B * (G), for G = ©i Gi, a bounded abelian 2-group, where G, is a direct sum of r copies of a cyclic group of order 2". The cases r = 1 and r = k, for some natural number k, are respectively considered in this paper.Item Projective resolutions and the homology of an induced group(2013) Olusa, O. S.; Ilori, S. A.; EniOluwafe, M.It is proved that the homology of an induced abelian group with coefficients in the different G– modules occuring in its projective resolution are isomorphic.