The number of fuzzy subgroups of a finite abelian \(p\)-group \(\mathbb{Z}_{p^{m}}\times \mathbb{Z}_{p^{n}}\). (English) Zbl 1358.20056
Summary: The main goal of this paper is to give formula for the number of fuzzy subgroups of a finite abelian group \(\mathbb{Z}_{p^{m}}\times \mathbb{Z}_{p^{n}}\) by using recurrence relation and extend the work of J. M. Oh [Iran. J. Fuzzy Syst. 10, No. 6, 125–135 (2013; Zbl 1343.20074)] using the concept which was already used by M. Tărnăuceanu and L. Bentea [Fuzzy Sets Syst. 159, No. 9, 1084–1096 (2008; Zbl 1171.20043)].
MSC:
| 20N25 | Fuzzy groups |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
| 05A15 | Exact enumeration problems, generating functions |
| 20D30 | Series and lattices of subgroups |
| 20K01 | Finite abelian groups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
