Score for the Group SL(2,38)
The set of all (n×n) non-singular matrices over the field F. And 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*...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2023-07-01
|
| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3017 |
| _version_ | 1797776174750892032 |
|---|---|
| author | Niran sabah Jasim Mohammed Ibrahem Lfta Ahmad Issa |
| author_facet | Niran sabah Jasim Mohammed Ibrahem Lfta Ahmad Issa |
| author_sort | Niran sabah Jasim |
| collection | DOAJ |
| description |
The set of all (n×n) non-singular matrices over the field F. And 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 rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this paper. We find the Artin indicator for this group after studying the rationally valued characters of the rational representations and the induced characters.
|
| first_indexed | 2024-03-12T22:46:10Z |
| format | Article |
| id | doaj.art-75fd89bbd2914b5aad623e2553bbfef0 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-03-12T22:46:10Z |
| publishDate | 2023-07-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-75fd89bbd2914b5aad623e2553bbfef02023-07-21T05:07:13ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072023-07-0136310.30526/36.3.3017Score for the Group SL(2,38)Niran sabah Jasim0Mohammed Ibrahem Lfta 1Ahmad Issa 2niversity of Baghdad, Faculty of Education for Pure Science /Ibn AL-Haytham, Department of MathematicsDepartment of Mathematics, Ministry of Education, Directorate General of Education karkh 3, Baghdad, Iraq. Department of Mathematics, Faculty of Science, Karabük University, Karabük, Türkiye The set of all (n×n) non-singular matrices over the field F. And 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 rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this paper. We find the Artin indicator for this group after studying the rationally valued characters of the rational representations and the induced characters. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3017 |
| spellingShingle | Niran sabah Jasim Mohammed Ibrahem Lfta Ahmad Issa Score for the Group SL(2,38) Ibn Al-Haitham Journal for Pure and Applied Sciences |
| title | Score for the Group SL(2,38) |
| title_full | Score for the Group SL(2,38) |
| title_fullStr | Score for the Group SL(2,38) |
| title_full_unstemmed | Score for the Group SL(2,38) |
| title_short | Score for the Group SL(2,38) |
| title_sort | score for the group sl 2 38 |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3017 |
| work_keys_str_mv | AT niransabahjasim scoreforthegroupsl238 AT mohammedibrahemlfta scoreforthegroupsl238 AT ahmadissa scoreforthegroupsl238 |