×

The fuzzy subgroups for the abelian structure \(\mathbb{Z}_8\times\mathbb{Z}_{2^n}\), \(n>2\). (English) Zbl 1477.20141

Summary: Any finite nilpotent group can be uniquely written as a direct product of \(p\)-groups. In this paper, we give explicit formulae for the number of distinct fuzzy subgroups of the Cartesian product of two abelian groups of orders \(2^n\) and 8 respectively for every integer \(n>2\).

MSC:

20N25 Fuzzy groups
20K01 Finite abelian groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups
PDFBibTeX XMLCite
Full Text: Link

References:

[1] Adebisi S.A. , M. Ogiugo and M. EniOluwafe (2020) Computing the Number of Distinct Fuzzy Subgroups for the Nilpotent p-Group ofD2n×C4International J.Math. Combin.Vol.1(2020),86-89. · Zbl 1477.20141
[2] Mashinchi M. , Mukaidono M.(1992). A classification of fuzzy subgroups. Ninth Fuzzy System Symposium, Sapporo, Japan, 649-652.
[3] Tarnauceanu, Marius. (2009). The number of fuzzy subgroups of finite cyclic groups and Delannoy numbers, European J. Combin. (30), 283-289, doi: 10.1016/ j.ejc.2007.12.005. · Zbl 1161.20059
[4] Tarnauceanu Marius. (2011). Classifying fuzzy subgroups for a class of finite p-groups. “ALL CUZa” Univ. Iasi, Romania. · Zbl 1240.20035
[5] Tarnauceanu, Marius. (2012). Classifying fuzzy subgroups of finite nonabelian groups. Iran.J.Fussy Systems. (9) 33-43.
[6] Tarnauceanu, Marius. , Bentea, L. (2008). A note on the number of fuzzy subgroups of finite groups, Sci. An. Univ. “ALL.Cuza” Iasi, Matt., (54) 209-220. · Zbl 1158.20039
[7] Tarnauceanu, Marius. , Bentea, L. (2008). On the number of fuzzy subgroups of finite abelian groups, Fuzzy Sets and Systems (159), 1084-1096, doi:10.1016/j.fss.201 7.11 · Zbl 1171.20043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.