Outcome for the group SL(2,57)

Author:

S Niran Sabah Jasim,Mohammed Salah Aldeen Zidan ,Azza I.M.S. Abu-Shams ,Ahmad Issa

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.

Publisher

College of Education for Pure Science (Ibn Al-Haitham)

Reference30 articles.

1. 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.

2. 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.

3. Algebra

4. 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.

5. Score for the Group SL(2,38)

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