Keywords:-
Article Content:-
Abstract
In this work we employ a combinatorial process to establish the intransitivity of a non-deranged permutation group . This provide for further study of some properties of the group thus, revealing that the average fixed points of every equals the number of orbits of . The study also deduce that the sum coefficients of cycle index polynomial of is unity.
References:-
References
Ibrahim A.A. (2004). Group Theoretical interpretation of Bara'at model. Retrieved from Mathematical Association of Nigeria, Proceedings of Annual National Conference, 35-46.
Ibrahim, A.A, Ejima O., and Kazeem O.A. (2016). On the Representations of Γ_1-Nonderanged Permutation Group G_p. Advances in Pure Mathematics, 6, 608-614.
Garba, A.I., and Ibrahim, A.A. (2010). A new method of constructing a variety of finite group based on some succession scheme. International Journal of Physical Science, (2)(3), 23-26.
Usman A. and Ibrahim A.A. (2011). A New Generating Function for Aunu Patterns: Application in Integer Group modulo n. Nigerian Journal of Basics and Applied Science, 19(1):1 -4.
Garba, A.I. and Abubakar, J. (2015). Construction of algebraic structure using a concatenation map. Nigerian Journal of Basic and Applied Sciences, (23)(2), 117-120.
Usman, A., and Magami, M.S., (2015). An Analysis of Group Theoretic Properties of a Class of (123)-avoiding pattern of Aunu Number using Thin Cycle Design. Mathematical Theory and Modelling, Vol.5, No 5.
Chun, P.B., Ibrahim, A.A, and Garba, A.I., (2016). Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of Aunu Permutations: Applications in the Generation and Analysis of a General Cyclic Code. Computer Science and Information Technology, 4(2): 45-47.
Ahmed, R.(2017). On the wreath product of Γ_1 non-deranged permutation group. Msc. Dissertation. Usmau Danfodiyo University, Sokoto, Nigeria.
Garba, A.I, Mustafa, A. and Suleiman, I. (2019). On Some Permutation Statistics of the Aunu Pattern ω_i∈G_p. Annals Computer Science Series, Vol. XVII. Fasc-2. 36-38.
Ibrahim, M, Ibrahim, A.A and Magami, M.S., (2014). On Block Design and Special Class of (123)-avoiding Aunu Permutation Pattern: A Slanted Flag Model. IOSR Journal of Mathematics, 10(3), 54-57.
Chun, P. B., Ibrahim, A. A and Magami, M.S., (2018). A [49 16 6] Linear Code as Product of the [7 4 2] Code Due to Aunu and the Hamming [7 4 3] Code. General Latters In Mathematics, 4(3), 114-119.
Garba, A.I., Yusuf, A., and Hassan, A., (2018). Some Topological Properties of a Constructed Structure. Journal of the Nigerian Association of Mathematical Physics, Vol.45, pp. 21-26.
Suleiman I, Ibrahim A. A and Ejima O. (2019). On the Addition Modulus of the Aunu Pattern ω_i∈G_p: An Investigation of Some Topological Properties. J Phys Math, 10: 299.
Suleiman, I., Garba, A.I. and Mustafa, A, (2020). On Some Non-deranged Permutation: A New Method of Construction. International Journal of Research-Granthaalayah, Vol.8, 3 309-314.