Tetrabonacci Subgroup of the Symmetric Group
over the Magic Squares Semigroup

Babayo A.M.; G.U.Garba

doi:https://doi.org/10.14445/22315373/IJMTT-V16P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 16 | Number 1 | Year 2014 | Article Id. IJMTT-V16P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V16P508

Tetrabonacci Subgroup of the Symmetric Group over the Magic Squares Semigroup

Babayo A.M., G.U.Garba

Citation :

Babayo A.M., G.U.Garba, "Tetrabonacci Subgroup of the Symmetric Group over the Magic Squares Semigroup," International Journal of Mathematics Trends and Technology (IJMTT), vol. 16, no. 1, pp. 46-51, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V16P508

Abstract

By the Loubere Magic Squares, we understand the set of magic squares constructed with the De La Loub Procedure. It is seemingly very close to triviality that this set equipped with the matrix binary operation of addition forms a semigroup if the underlining set or multi set so considered in the square is of the natural numbers. In this paper, we introduce the permutation and its composition over the Loub Magic Squares Semigroup logically to form a subgroup of the Symmetric Group which by analogy to the Fibonacci Group is termed the Tetrabonacci Group. We also present a new definition, a new procedure and a new generalization of the Loubere.

Keywords

Permutations, Sequences, Cycles, Effects, Groups, Semigroups

References

[1] Sreeranjini K. S. and V. Madhukar Mallayya. Semi Magic Constants as a Field, International Journal of Mathematical Sciences and Applications, vol. 2, pp. 799, 2012.
[2] E.Arnold, R. Field, S. Lucas and L. Taalman. Minimal Complete Shidoku Symmetry Groups, Journal of Combinatorial Mathematics and Combinatorial Computing, (Available on http/educ-jmu.edu/arnoldea/JCMCC. Pdf- to appear), pp.1, 2012.
[3] Allan Adler. Magic N-Cubes Form a Free Monoid, the Electronic Journal of Combinatorics, vol. 4, pp1, 1997.
[4] Colin M. Cambell, Edmund F. Robertson, Nikola Ru kuc, Richard M. Thomas. Fibonacci Semigroups, Journal of Pure and Applied Algebra, vol. 94, pp. 49, 1994.
[5] A. R. Vasistha and A. K. Vasistha. Modern Algebra (Abstract Algebra), Krishna Parakashan Media(P) Ltd, Meerut, Delhi, vol. 52, pp. 93-102, 2006.
[6] B. Sree Johannathan. Magic Squares for All Success, (Available on www.spritualmindpower.com), 2005.
[7] Gan Yee Siang, Fong Win Heng, Nor Haniza Sarmin. Properties and Solutions of Magic Squares. Menemui Matematik ( Discovering Mathematics), vol. 34, pp. 66, 2012.
[8] A. Umar. Lead Paper: Some Remarks about Fibonacci Groups and Semigroups, Nigerian Mathematical Society Annual Conference, A.B.U.Zaria, Nigeria, pp. 1 – 33, 2012. (un published)
[9]Joseph J. Rotman. A First Course in Abstract Algebra, Prentice Hall, Upper Saddle River, New Jersey , vol. 4, pp. 134, 20.
[10] John M. Howie. Fundamentals of Semigroup Theory, Oxford University Press, New York, United States, vol. 1, pp.1, 2003.