Document Type : Research Paper
Authors
1 Department of Mathematics, Faculty of Science, University of Lagos, Nigeria.
2 Department of Mathematics, Faculty of Science, University of Ibadan, Nigeria.
Abstract
A group is nilpotent if it has a normal series of a finite length n. By this notion, every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. In this paper, the explicit formulae is given for the number of distinct fuzzy subgroups of the Cartesian product of the dihedral group of order 23 with a cyclic group of order of an m power of two for, which m ≥ 3.
Keywords
- Finite p-groups
- Nilpotent group
- Fuzzy subgroups
- Dihedral group
- Inclusion-exclusion principle
- Maximal subgroups
Main Subjects
- Bhunia, S., Ghorai, G., Xin, Q., & Torshavn, F. I. (2021). On the characterization of Pythagorean fuzzy subgroups. AIMS mathematics, 6(1), 962-978.
- Mashinchi, M., & Mukaidono, M. (1993). On fuzzy subgroups classification. Research reports of meiji univ, (9), 31-36.
- Murali, V., & Makamba, B. B. (2003). On an equivalence of fuzzy subgroups III. International journal of mathematics and mathematical sciences, 2003(36), 2303-2313.
- Ndiweni, O. (2018). Classification of distinct fuzzy subgroups of the dihedral group D pnq for p and q distinct primes and n 2 N (Ph.D Thesis, University of Fort Hare). Retrieved from http://vital.seals.ac.za:8080/vital/access/services/Download/vital:39997/SOURCE1
- Tărnăuceanu, M. (2009). The number of fuzzy subgroups of finite cyclic groups and Delannoy numbers. European journal of combinatorics, 30(1), 283-287.
- Tarnauceanu, M. (2011). Classifying fuzzy subgroups for a class of finite p-groups. Retrieved from https://www.math.uaic.ro/~martar/pdf/articole/articol%2058.pdf
- Tarnauceanu, M. (2012). Classifying fuzzy subgroups of finite nonabelian groups. Iranian journal of fuzzy systems, 9(4), 31-41.
- Bentea, L., & Tarnauceanu, 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.
- Thompson, J. M. T. (1995). Progress in nonlinear dynamics and chaos. In Kounadis, A. N., Krätzig, W.B. (Eds.), Nonlinear Stability of Structures. International Centre for Mechanical Sciences, vol 342. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4346-9_5
- Adebisi, S. A., Ogiugo, M., & Enioluwafe, M. (2020). On the p-groups of the algebraic structure of D2n× C8. Mathematical combinatorics, 3, 102-105.
- 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. and EniOluwafe M. (2020) Determining the number of distinct fuzzy subgroups for the abelian structure : Z. Trasection of the Nigerian association of mathematical physics, 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.
- Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
- Rosenfield, R. L. (1971). Plasma testosterone binding globulin and indexes of the concentration of unbound plasma androgens in normal and hirsute subjects. The journal of clinical endocrinology & metabolism, 32(6), 717-728.
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