Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2018.08.10
  • Accepted : 2018.10.12
  • Published : 2019.10.31
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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.

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References

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