Computing fuzzy subgroups of some special cyclic groups
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1049-1067
Published online October 31, 2019
Babington Makamba, Michael M. Munywoki
University of Fort Hare; Technical University of Mombasa
Abstract : In this paper, we discuss the number of distinct fuzzy subgroups of the group $\mathbb{Z}_{p^n}\times \mathbb{Z}_{q^m}\times \mathbb{Z}_r$, $m=1,2,3$ where $p,q,r$ are distinct primes for any $n\in \mathbb{Z}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group $G$ and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.
Keywords : maximal chain, equivalence, fuzzy subgroups
MSC numbers : Primary 20N25, 03E72; Secondary 20K01, 20K27
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