THE NUMBER OF DISTINCT FUZZY SUBGROUPS OF THE GROUP $\mathbb{Z}_{p^n} \times \mathbb{Z}_{q^m} \times \mathbb{Z}_r$ FOR DISTINCT PRIMES $p, q, r$ AND $m, n \in \mathbb{Z}^{+}$
Keywords:
maximal chain, equivalence, fuzzy subgroups.DOI:
https://doi.org/10.17654/0973421X22006Abstract
The equivalence relation ' $\sim$ ' defined by Murali and Makamba is used to find the number of the distinct fuzzy subgroups of the group $\mathbb{Z}_{p^n} \times \mathbb{Z}_{q^m} \times \mathbb{Z}_r$, where $p, q, r$ are distinct primes with $m$ and $n$ as positive integers. Using the criss-cut method explained in this paper, explicit formulae are presented.
Received: October 25, 2021
Accepted: November 30, 2021
References
M. Munywoki and B. Makamba, Computing fuzzy subgroups of some special cyclic groups, Commun. Korean Math. Soc. 34(4) (2019), 1049-1067. https://www.koreascience.or.kr/article/JAKO201931765048953.do.
V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups i, Fuzzy Sets and Systems 123(2) (2001), 259-264.
https://www.sciencedirect.com/science/article/abs/pii/S0165011400000981.
V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups ii, Fuzzy Sets and Systems 136(1) (2003), 93-104.
https://www.sciencedirect.com/science/article/abs/pii/S0165011402001409.
V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order Fuzzy Sets and Systems 144(3) (2004), 459-470. https://www.sciencedirect.com/science/article/abs/pii/S0165011403002240.
V. Murali and B. B. Makamba, On methods of counting preferential fuzzy subgroups, Advances in Fuzzy Sets and Systems 3(1) (2008), 21-42. http://www.pphmj.com/abstract/2955.htm.
O. Ndiweni, The classification of some fuzzy subgroups of finite groups under a natural equivalence and its extension, with particular emphasis on the number of equivalence classes, MS Thesis, University of Fort Hare, Alice, South Africa, 2007.
O. Ndiweni and B. B. Makamba, Distinct fuzzy subgroups of some dihedral groups, Advances in Fuzzy Sets and Systems 9(1) (2011), 65-91. http://www.pphmj.com/abstract/6155.htm.
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35(3) (1971), 512-517. https://www.sciencedirect.com/science/article/pii/0022247X71901995.
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