Result for the group SL(2,172)

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Published: Apr 20, 2024
DOI: https://doi.org/10.30526/37.2.3015

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Ghofran Awad Khalaf
Ministry of Education, Directorate General of Education in Diyala, Diyala, Iraq
https://orcid.org/0009-0005-1045-2777
Niran Sabah Jasim
Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham University of Baghdad, Baghdad, Iraq
https://orcid.org/0000-0001-5340-3020
Zeinab Saeidian
University of Kashan, Kashan, Iran
https://orcid.org/0000-0002-6279-7217
Azza I.M.S. Abu-Shams
Mathematics of Department, College of Science, Philadelphia University, Amman, Jordan
https://orcid.org/0009-0003-1741-1447

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 n over the field F, denoted by GL(n,F). The determinant of these matrices is a homomorphism from GL(n,F) into F* and the kernel of this homomorphism was the special linear group and denoted by SL(n,F). Thus SL(n,F) is the subgroup of GL(n,F) 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 SL(2,17^2 ) discuss in this work and find the Artin indicator for this group after study the rational valued characters of the rational representations and the induced characters. 

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Result for the group SL(2,172). (2024). Ibn AL-Haitham Journal For Pure and Applied Sciences, 37(2), 440-446. https://doi.org/10.30526/37.2.3015
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Vol. 37 No. 2 (2024)
Section
Mathematics
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Result for the group SL(2,172). (2024). Ibn AL-Haitham Journal For Pure and Applied Sciences, 37(2), 440-446. https://doi.org/10.30526/37.2.3015
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