Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Lagos, Nigeria.

2 Department of Mathematics, School of Science, Yaba College of Technology, Nigeria.

3 Department of Mathematics, Faculty of Science, University of Ibadan, Nigeria.

Abstract

Every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. Efforts are carefully being intensified to calculate, in this paper, the explicit formulae for the number of distinct fuzzy subgroups of the cartesian product of the dihedral group of order  with a cyclic group of order of an m power of two for, which n >5.

Keywords

Main Subjects

  • Mashinchi, M., & Mukaidono, M. (1992). A classification of fuzzy subgroups. Ninth Fuzzy System Symposium (pp. 649-652). Sapporo, Japan.
  • Mashallah, M., & Masao, M. (1993). On fuzzy subgroups classification. Research reports, school of science and technology, Meiji University, (9), 31-36. https://cir.nii.ac.jp/crid/1520009410152402816
  • Murali, V., & Makamba, B. B. (2003). On an equivalence of fuzzy subgroups III. International journal of mathematics and mathematical sciences, 2003(36), 2303-2313. https://doi.org/10.1155/S0161171203205238
  • Ndiweni, O. (2014). The classification of fuzzy subgroups of the dihedral group dn, for n a product of distinct prime numbers (Doctoral dissertation, University of Fort Hare).‏ Retrieved from https://core.ac.uk/download/pdf/145052731.pdf
  • Tărnăuceanu, M. (2009). The number of fuzzy subgroups of finite cyclic groups and Delannoy numbers. European journal of combinatorics, 30(1), 283-287. https://doi.org/10.1016/j.ejc.2007.12.005
  • Tărnăuceanu, M. (2013). Classifying fuzzy subgroups for a class of finite p-groups. Critical review7, 30-39.
  • Tărnăuceanu, M. (2012). Classifying fuzzy subgroups of finite nonabelian groups. Iranian journal of fuzzy systems, 9(4), 31-41. https://ijfs.usb.ac.ir/article_131_a85ac48a21fd8e1c3315ef08068da1fe.pdf
  • Bentea, L., & Tărnăuceanu, M. (2008). A note on the number of fuzzy subgroups of finite groups. Stiint. Univ. Al. I. Cuza Ias, Ser. Noua, Mat, 54(1), 209-220.
  • Tărnăuceanu, M., & Bentea, L. (2008). On the number of fuzzy subgroups of finite abelian groups. Fuzzy sets and systems, 159(9), 1084-1096. https://doi.org/10.1016/j.fss.2007.11.014
  • Zadeh, L. A. (1965). Fuzzy sets. Information and control8(3), 338-353.
  • Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications35(3), 512-517.
  • Adebisi, S. A., Ogiugo, M., & EniOluwafe, M. (2020). Computing the number of distinct fuzzy subgroups for the nilpotent p-Group of D2n× C4. International J. Math. Combin, 1, 86-89.
  • Adebisi, S. A., Ogiugo, M., & EniOluwafe, M. (2020). Determining the number of distinct fuzzy subgroups for the abelian structure: Z4× Z2n− 1, n> 2. NAMP, 11, 5-6.
  • Adebisi, S. A., & Enioluwafe, M. (2020). An explicit formula for the number of distinct fuzzy subgroups of the cartesian product of the Dihedral group of order 2n with a cyclic group of order 2. Universal Journal of mathematics and mathematical sciences, 13(1), 1-7. http://dx.doi.org/10.17654/UM013010001
  • Adebisi, S. A., Ogiugo, M., & Enioluwafe, M. (2022). The fuzzy subgroups for the nilpotent (p-group) of (d23× c2m) for m≥ 3. Journal of fuzzy extension and applications, 3(3), 212-218.
  • Das, P. S. (1981). Fuzzy groups and level subgroups.  math. analy. and applic.84(1), 264-269. https://core.ac.uk/download/pdf/82494773.pdf
  • Berkovich, Y., & Janko, Z. (2008). Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order. Volume 2(Vol. 47). Walter de Gruyter.