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

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 induce

Fumonisin B1 (FB1) is a mycotoxin produced in some grains (mainly corn) by Fusarium species. Due to a structural similarity between FB1 and sphinganine, sphingolipids metabolism is inhibited. Such inhibition plays a critical role in cell to cell singling and structure of lipoprotein; therefore FB1 has been suggested to have a relationship with human and animal cancer. This research is planned to study the effect of FB1 on male mice at two doses (20 and 30 µg/ ml) on the expression of TGF-β1 and p16 in liver cells. Three groups of Swiss albino male mice; each group was orally administrated with FB1 toxin as the following: normal saline (control group); 20 and 30 µg/ ml. All groups were sacrificed after two weeks of oral manage