Counting the Number of Fuzzy Subgroups of Abelian Group $$G= {\mathbb {Z}}_{p^n}\times {\mathbb {Z}}_{p^m}$$

2021 ◽  
pp. 499-509
Author(s):  
R. Ameri ◽  
A. Kialashaki
Keyword(s):  
Abelian Group ◽  
Fuzzy Subgroups

Fuzzy subgroups of non–abelian group Zpn ⋊ Zp for any prime p

2019 ◽  
Author(s):  
Agin Kumari ◽  
Preeti ◽  
Amit Sehgal ◽  
P. K. Sharma ◽  
Sarita Sehgal
Keyword(s):  
Abelian Group ◽  
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.

FUZZY SUBGROUPS OF A FINITE ABELIAN GROUP Z(p^mq^r) \times Z(p^n)

2017 ◽  
Vol 21 (4) ◽  
pp. 291-302 ◽  
Author(s):  
Amit Sehgal ◽  
Sarita Sehgal ◽  
P. K. Sharma ◽  
Manjeet Jakhar
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Fuzzy Subgroups

Counting the number of fuzzy subgroups of an abelian group of order pnqm

2004 ◽  
Vol 144 (3) ◽  
pp. 459-470 ◽  
Author(s):  
V. Murali ◽  
B.B. Makamba
Keyword(s):  
Abelian Group ◽  
Fuzzy Subgroups

SIMILARITY RELATIONS, VAGUE GROUPS, AND FUZZY SUBGROUPS

2006 ◽  
Vol 02 (03) ◽  
pp. 195-208
Author(s):  
KIRAN R. BHUTANI ◽  
JOHN N. MORDESON
Keyword(s):  
Abelian Group ◽  
Similarity Relations ◽  
Numerical Invariants ◽  
Fuzzy Subgroups

We define vague groups in terms of similarity relations rather than fuzzy equalities. This yields a bijection between the set of all right-invariant similarity relations on a group and the set of all fuzzy subgroups of the group. Under this bijection, right-invariant and left-invariant similarity relations correspond to normal fuzzy subgroups. We show how this bijection allows for the transfer of results between vague groups and fuzzy subgroups. In particular, certain numerical invariants that characterize fuzzy subgroups of an Abelian group can be used to characterize vague groups.

Sign in / Sign up

Export Citation Format

Share Document