Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE NUMBER OF FUZZY SUBGROUPS OF ℤpm × ℤpn × ℤpℓ

  • OH, JU-MOK (Mathematics, Gangneung-Wonju National University) ;
  • HWANG, KYUNG-WON (Department of Mathematics, Mathematics, Dong-A University) ;
  • SIM, IMBO (Mechanical Engineering, Dong-A University)
  • Received : 2022.07.23
  • Accepted : 2022.09.07
  • Published : 2022.09.30
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Abstract

In this paper we are concerned with the number of fuzzy subgroups of a finite abelian p-group ℤpm × ℤpn × ℤpℓ of rank three with order pm+n+ℓ. We obtain a recurrence relation for the number of fuzzy subgroups of a finite abelian p-group ℤpm × ℤpn × ℤpℓ. In order to show that using this recurrence relation, one can find explicit formulas for the number of fuzzy subgroups of ℤpm × ℤpn × ℤpℓ consecutively, we give explicit formulas for the number of fuzzy subgroups of ℤpm × ℤpn × ℤpℓ where (n, ℓ) = (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2), (5, 2).

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Acknowledgement

This work was supported by the Dong-A university research fund.

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