Fuzzy Subgroups of Abelian Groups

2005 ◽  
pp. 139-166
Author(s):  
John N. Mordeson ◽  
Kiran R. Bhutani ◽  
Azriel Rosenfeld
Keyword(s):  
Abelian Groups ◽  
Fuzzy Subgroups

scholarly journals The Number of Subgroup Chains of Finite Nilpotent Groups

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1537 ◽  
Author(s):  
Lingling Han ◽  
Xiuyun Guo
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Recursive Formula ◽  
Nilpotent Groups ◽  
Classification Problem ◽  
Finite Abelian Groups ◽  
Counting Problem ◽  
Cyclic Groups ◽  
Fuzzy Subgroups

In this paper, we mainly count the number of subgroup chains of a finite nilpotent group. We derive a recursive formula that reduces the counting problem to that of finite p-groups. As applications of our main result, the classification problem of distinct fuzzy subgroups of finite abelian groups is reduced to that of finite abelian p-groups. In particular, an explicit recursive formula for the number of distinct fuzzy subgroups of a finite abelian group whose Sylow subgroups are cyclic groups or elementary abelian groups is given.

scholarly journals Pinned-flags of some operations on fuzzy subgroups

2005 ◽  
Vol 2005 (23) ◽  
pp. 3819-3826
Author(s):  
B. B. Makamba ◽  
V. Murali
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Fuzzy Subgroups

Fuzzy subgroups of finite groups have been treated recently using the concept of pinned-flags. In this paper, we consider the operations of intersection, sum, product, and quotient of fuzzy subgroups of finite abelian groups in general, in terms of pinned-flags. We develop algorithms to construct pinned-flags of fuzzy subgroups corresponding to these operations and prove their validity. We illustrate some applications of such algorithms.

On the number of fuzzy subgroups of finite abelian groups

2008 ◽  
Vol 159 (9) ◽  
pp. 1084-1096 ◽  
Author(s):  
Marius Tărnăuceanu ◽  
Lucian Bentea
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Fuzzy Subgroups

Distributivity and pseudocomplementation of lattices of generalized \(L\)-subgroups

2016 ◽  
Vol 5 (2) ◽  
pp. 107 ◽  
Author(s):  
Dilek Bayrak ◽  
Sultan Yamak
Keyword(s):  
Cyclic Group ◽  
Abelian Groups ◽  
Study Groups ◽  
Finite Cyclic Group ◽  
Pseudocomplemented Lattice ◽  
Fuzzy Subgroups

The main goal of this paper is to study the lattice of \((0,\mu)\)-\(L\)-subgroups of a group. We characterize abelian groups by the lattice of \((0,\mu)\)-\(L\)-subgroups. Also, we show that a group $G$ is locally cyclic if and only if the lattice of \((0,\mu)\)-\(L\)-subgroups is distributive. As consequence, we obtain that the lattices of all \((\in,\in\vee q)\)-fuzzy subgroups and all fuzzy subgroups of a finite cyclic group are distributive. Finally, we study groups which of the lattice of \((\lambda,\mu)\)-\(L\)-subgroups is pseudocomplemented lattice.

A characterization of fuzzy subgroups of some Abelian groups

1994 ◽  
Vol 80 (3-4) ◽  
pp. 243-252 ◽  
Author(s):  
Jae-Gyeom Kim ◽  
Han-Doo Kim
Keyword(s):  
Abelian Groups ◽  
Fuzzy Subgroups

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

2021 ◽  
Vol 6 (3) ◽  
pp. 45
Author(s):  
Sunday Adesina Adebisi ◽  
Mike Ogiugo ◽  
Michael Enioluwafe
Keyword(s):  
Abelian Groups ◽  
Large Order ◽  
Fuzzy Subgroups

Equivalence of Fuzzy Subgroups of Finite Abelian Groups

2005 ◽  
pp. 201-238
Author(s):  
John N. Mordeson ◽  
Kiran R. Bhutani ◽  
Azriel Rosenfeld
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Fuzzy Subgroups
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