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http://dx.doi.org/10.4134/CKMS.c180341

COMPUTING FUZZY SUBGROUPS OF SOME SPECIAL CYCLIC GROUPS  

Makamba, Babington (Department of Mathematics University of Fort Hare)
Munywoki, Michael M. (Department of Mathematics and Physics Technical University of Mombasa)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1049-1067 More about this Journal
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;
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