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
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