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The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups

Sunday Adesina Adebisi, Mike Ogiugo, Michael Enioluwafe
2021 Mathematics and Computer Science  
In this paper, the fuzzy subgroups of the nilpotent product of two abelian subgroups of orders 2 n and 128.  ...  Some methods were once being used in counting the chains of fuzzy subgroups of an arbitrary finite p-group G.  ...  His work so far has been able to give some relevant clue on the classification of fuzzy subgroups for a class of finite p-groups including some abelian, elementary abelian as well as the so called non-abelian  ... 
doi:10.11648/j.mcs.20210603.11 fatcat:g5kxjqgumzclzpxfjhlf7fahli

Page 5303 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
and is said to be a T-fuzzy subgroup or simply a fuzzy subgroup of G if yw is symmetric, u(xy) > u(x)Ty(y) for all x, y € G, and u(e) = 1. Let ht bea fuzzy subgroup of G and yw; = {x € G| u(x) =1}.  ...  Let the torsion subgroup of an abelian topological group G be everywhere dense in it.  ... 

Page 1353 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Summary: “We define and determine basic properties of torsion, primary, divisible, and pure fuzzy subgroups of an abelian group. We characterize these fuzzy subgroups in terms of level subgroups.  ...  Application to the class of P-hypergroups is given.” 92¢:20136 20N25 04A72 Malik, D.S. (1-CREI); Mordeson, John N. (1-CREI) Fuzzy subgroups of abelian groups. Chinese J.  ... 


Muhammad Gulzar, Dilshad Alghazzawi, M. Haris Mateen, Nasreen Kausar
2020 IEEE Access  
Solairaju and Mahalakshmi [34] investigated some characterization of hesitant intuitionistic fuzzy soft set and presented the idea hesitant intuitionistic fuzzy soft group. Latif et al.  ...  We also introduce the idea of t-intuitionistic fuzzy Abelian subgroups and t-intuitionistic fuzzy cyclic subgroups and prove that every t-intuitionistic fuzzy subgroup of Abelian (cyclic) group is t-intuitionistic  ...  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  ... 
doi:10.1109/access.2020.3020366 fatcat:wc44q7psx5aa3m4b6mf4kylo3m

Page 4247 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
Some fundamental properties of one such viable fuzzy subgroup are obtained.” 93h:20080 20N25 04A72 Filep, Laszl6 (H-TTCN) Structure and construction of fuzzy subgroups of a group.  ...  4247 with a fuzzy set, some new concepts of fuzzy subgroup are intro- duced and their acceptability is investigated.  ... 

Page 8350 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Comer (1-CITA; Charleston, SC) 99m:20164 20N25 Kim, Jae-Gyeom (KR-K YSU; Pusan); Kim, Han-Doo (KR-INJ; Kimhae) Some characterizations of fuzzy subgroups: via fuzzy p*-subsets and fuzzy p*-subgroups.  ...  They use this notion to characterize fuzzy subgroups and show that every commutative fuzzy subgroup is characterized as the intersection of all its minimal p*-subgroups.  ... 

Page 3646 of Mathematical Reviews Vol. , Issue 93g [page]

1993 Mathematical Reviews  
As an indispensable tool, the characterization of a fuzzy normal subgroup of a group by the so-called open level subgroups is brought forth.  ...  These examples also show that a fuzzy subgroup of a group G need not be a fuzzy direct sum of subgroups whose supports are cyclic even if G is a direct sum of cyclic groups.  ... 

The number of fuzzy subgroups of a finite abelian group of order p^nq^m [article]

Lingling Han, Xiuyun Guo
2019 arXiv   pre-print
The purpose of this paper is to determine the number of fuzzy subgroups of a finite abelian group of order p^nq^m.  ...  As an application of our main result, explicit formulas for the number of fuzzy subgroups of Z_p^n×Z_q^m and Z_p^n×Z_q^m are given.  ...  It could help to characterize the fuzzy subgroup of a group G by using the level subsets. The fuzzy subgroups of a group can be classified up to some natural equivalence relations.  ... 
arXiv:1904.06642v1 fatcat:4yrzyeq42fcw7gxxfaswcaueky

Page 7867 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
A monothetic group is a Hausdorff group with a dense cyclic subgroup. Such a group is of course abelian.  ...  In particular, compact abelian groups for which TD attains the least or the greatest possible values (the weight and the cardinality of G, respectively) are characterized and, for compact connected groups  ... 

Page 6896 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
On an abelian group G without torsion, cardG < 2° (c is the cardinality of the continuum), a topology is constructed such that any cyclic subgroup can be isomorphic to only a finite number of subgroups  ...  In this paper the author characterizes the class K, of all compact groups which do not contain subgroups isomorphic to ZN .  ... 

Page 170 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
Summary: “We introduce the concept of the small invariant fuzzy neighborhood groups (SIFN-groups) to characterize fuzzy neigh- borhood groups for coincidence of the left and right fuzzy uni- formities.  ...  We say that the closed subgroup H of a locally compact abelian (LCA) group G splits in G if G contains a closed subgroup K such that HN K = {0}, the identity of G, and the map (h,k) +h+k is a homeomorphism  ... 

Page 1411 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Kumbhojkar (6-SHIV; Kolhapur) 95¢:20111 20N25 04A72 Kim, Jae-Gyeom; Kim, Han-Doo A characterization of fuzzy subgroups of some abelian groups. (English summary) Inform.  ...  20N25 Kim, Jae-Gyeom Fuzzy subgroups of finite groups and abelian groups.  ... 

Page 7350 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
Fuzzy Math. 3 (1995), no. 4, 833-849. The author gives a definition of a fuzzy subgroup [resp. subring or ideal] of a fuzzy group [resp. ring] and proves some standard results.  ...  In this paper the authors give a necessary and sufficient condition for the union of fuzzy subgroups of a group G to be a fuzzy subgroup of G. Let {y;}ic, be a collection of fuzzy subgroups of G.  ... 

The number of fuzzy subgroups of finite cyclic groups and Delannoy numbers

Marius Tărnăuceanu
2009 European journal of combinatorics (Print)  
The main goal of this note is to establish a connection between the fuzzy subgroups of a finite cyclic group with k direct factors and the lattice paths of Z k .  ...  Acknowledgements The author is grateful to the reviewers for their remarks which improved the previous version of the paper.  ...  Even for some particular classes of finite groups, as finite abelian groups, the problem of counting the number of distinct fuzzy subgroups is very difficult.  ... 
doi:10.1016/j.ejc.2007.12.005 fatcat:fdkvzqyimve4hgzpocvp6zn74q

Page 7058 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
Every maximal finite-valued /-subgroup of an abelian /-group is contained in a maximal almost finite-valued /-subgroup. W. C.  ...  The finite-valued radical of an /-group is contained in every maximal almost finite-valued /-subgroup. Theorem B. A maximal almost finite-valued /-subgroup of an abelian /-group is saturated.  ... 
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