Outcome for the group SL(2,57)

Article Sidebar

PDF
Published: Jan 20, 2024
DOI: https://doi.org/10.30526/37.1.3018

Main Article Content

Niran Sabah Jasim
University of Baghdad, College of Education for Pure Science Ibn Al-Haitham, Department of Mathematics, Baghdad, Iraq.
Mohammed Salah Aldeen Zidan
Ministry of Education, Directorate General of Education karkh 1, Baghdad, Iraq.
Azza I.M.S. Abu-Shams
Philadelphia University, College of Science, Mathematics Department, Ammaan Jordan
Ahmad Issa
Karabük University, Faculty of Science, Department of Mathematics, Karabük, Türkiye.

Abstract

The set of all (n×n) non-singular matrices over the field F this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension  over the field F, denoted by . The determinant of these matrices is a homomorphism from  into F* and the kernel of this homomorphism was the special linear group and denoted by  Thus  is the subgroup of  which contains all matrices of determinant one.


The rational valued characters of the rational representations written as a linear combination of the induced characters for the groups  discuss in this paper and find the Artin indicator for this group after study the rational valued characters of the rational representations and the induced characters.

Article Details

How to Cite
Outcome for the group SL(2,57). (2024). Ibn AL-Haitham Journal For Pure and Applied Sciences, 37(1), 403-411. https://doi.org/10.30526/37.1.3018
Issue
Vol. 37 No. 1 (2024)
Section
Mathematics
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

licenseTerms

How to Cite

Outcome for the group SL(2,57). (2024). Ibn AL-Haitham Journal For Pure and Applied Sciences, 37(1), 403-411. https://doi.org/10.30526/37.1.3018
Crossref
Scopus
Google Scholar
Europe PMC

Publication Dates

References

Mohamed, S K. On Rational -Valued Characters of Certain Types of Permutation Group. Ibn Al-Haitham journal for pure and applied sciences 2006, 19(4), 99-108.

Saad, O. B. Investigating Particular Representations for Matrix Lie GroupsSO(3) andSL(2,₵). Iraqi journal of Science 2019, 60(4), 856-858, DOI: 10.24996/ijs.2019.60.4.19.

Sigler, L.E. Algebra, 1976, Springer-Verlage, Berlin.

Niran, S. J.; Hadeel H. L; Rana N. M. Computations for the special linear group (2,49). Journal of Interdisciplinary Mathematics 2021, 24(6), 1677–1683, DOI: 10.1080/09720502.2021.1892273.

Mohammed I. L., Niran S. J., Issa A. Score for the group SL (2,38). Ibn Al-Haitham Journal for Pure and Applied Sciences 2023, 36(3), 408–415, DOI:10.30526/36.3.3017.

Noor Alhuda, S. S.; Niran S. J. Periodical split for the groups PSL(2,31) and PSL(2,37). Journal of Discrete Mathematical Sciences and Cryptography 2022, 25(2), 605–608, DOI : 10.1080/09720529.2021.1982490.

Sherouk, A. K.; Niran S. J. Calculation for the groups SL(2,U), U = 31 and 37. Journal of Discrete Mathematical Sciences and Cryptography 2022, 25(2), 609-613, DOI: 10.1080/09720529.2021.1972614.

Salih,O. M.; Mohammed,N. J.; Alwan,B. M. Result for the Groups SUT(2,p), where p = 3, 5, 7. Technology reports of Kansai university 2020, 62 (3), 2029-2034.

Dunya, M. H.; Ahmed, K. M.; Intidhar, Z. M. Score for some Groups SUT(2,p). Int. J. Nonlinear Anal. Appl. 2021, 12(2), 1-15.

Maha, A. M.; Lemya A. Al. H.; Asma A. A. New algorithm based on deep learning for number recognition. International Journal of Mathematics and Computer Science 2023, 18( 3), 429–438.

Anwar, K. F.; Lemya, A. Al. H.; Areej, M. A.; Shatha A. S. Symmetric generalized bi-derivations with prime ideals. International Journal of Mathematics and Computer Science 2023, 18(4), 675–684,.

Bill, C. Representations of SL2 (R). Pacific Journal of Mathematics 2020, 3(1), 231-250.

Yurii, I. L. Introduction to the Theory of Banach Representations of Groups 2021, Birkhäuser Verlag.

Chemistry, L. Representations of Groups 2019, Kharkov, Ukraine.

Zagier, D. Applications of the representation theory of finite groups 2019, New York.

Alexander, K. Jr. An introduction to Lie groups and Lie algebras 2022, Birkhäuser Verlag.

Reiner, I. Representation theory 2021, John Wiley & Sons, NewYork –London.

Kevin, H. on representation theory in groups, 2020, Springer-Verlage.

Mohammed, S. I.K.; Lemia, A. Al. H. The Artin' s Exponent of A Special Linear Group SL(2,2k ). Eng. & Tech. Journal 2010, 28(10), 1924-1934.

Yuxin, Z. T.; Orkesh, N.; Zhang, Z. Homology Algebra and Applications. J.Sci.I.R.Iran 2019, 3(5) 11-13.

Curtis, C.W. ; Reiner, I. The Representation Theory Of Finite Groups And Associative Algebras 1962, John Wiley & Sons, NewYork –London.

Behravesh, H. The Rational Character Table Of Special Linear Groups. J.Sci.I.R.Iran 1998, 9 (2), 173-180.

Behravesh, H. Quasi – Permutation Representations Of SL(n,q) And PSL(n,q). Glasgow.Math.J. 1999, 41, 393- 408.

Isaacs, I.M. Character Theory Of Finite Groups 1976, Academic Press, NewYork.

Serre, J.P. Linear Representation Of Finite Groups 1977, Springer-Verlage.

Gehles, K.E. Ordinary Characters Of Finite Special Linear Groups 2002, M.Sc. Thesis, Dissertation, University of St Andrews.

Kirdar, M.S. The Factor Group Of The Z-Valued Class Function Modulo The Group Of The Generalized Characters 1982, Ph.D.Thesis, University of Birmingham.

Kirdar, M.S. On Brauer’s Proof Of The Artin Induction Theorem. Abhath AL–Yarmouk (Basic Sciences and Engineering) journal 2002, 11(1A), 51–54.

Apostol, T.M. Introduction To Analytic Number Theory 1976, Springer-Verlage, NewYork.

Hall, B. C. Lie Groups, Lie Algebras, and Representations 2015, Springer.