On the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$
On the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$
Ju-Mok Oh(Gangneung-Wonju National University); Kyung-Won Hwang(Dong-A University); Imbo Sim(Dong-A University)
40권 5호, 1181~1198쪽
초록
In this paper we are concerned with the number of fuzzy subgroups of a finite abelian $p$-group $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ of rank three with order $p^{m+n+\ell}$. We obtain a recurrence relation for the number of fuzzy subgroups of a finite abelian $p$-group $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$. In order to show that using this recurrence relation, one can find explicit formulas for the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ consecutively, we give explicit formulas for the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ where $(n,\ell)=(1,1), (2,1), (3,1),(4,1), (5,1), (2,2), (3,2),(4,2),(5,2)$.
Abstract
In this paper we are concerned with the number of fuzzy subgroups of a finite abelian $p$-group $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ of rank three with order $p^{m+n+\ell}$. We obtain a recurrence relation for the number of fuzzy subgroups of a finite abelian $p$-group $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$. In order to show that using this recurrence relation, one can find explicit formulas for the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ consecutively, we give explicit formulas for the number of fuzzy subgroups of $\Z_{p^m}\times \Z_{p^n}\times \Z_{p^{\ell}}$ where $(n,\ell)=(1,1), (2,1), (3,1),(4,1), (5,1), (2,2), (3,2),(4,2),(5,2)$.
- 발행기관:
- 한국전산응용수학회
- 분류:
- 수학