The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

This study aims to show some of Imam Al-Bukhari's criticism of the Hadith from the Metn side, and part of his methodology in dealing with the correct hadiths that are tainted by a bug. This research focuses on what Imam Al-Bukhari summarized in his Sahih illusion of the narrator in his attribution, or uniqueness of the narrator, or to suggest a novel. We find that Bukhari sometimes abbreviates the hadeeth, and does not bring it out completely in his Sahih. He is satisfied with the abbreviated position but has done so because of a bug in it. The Bukhari usually does not declare his intention but knows this through tracking, inspection, and research of the correct hadiths.

The Interests of British Military in Iraq was not based upon unified vision for the Iraqi identity ,it worked on breaking that identity and deal with the different ethnic and religious minorities and tried to bring it to its side and use it and its figures in the governmental position ,the aim was to make these minorities and here to the Britain to achieve its purposes and strategies in Iraq also vowed to provoked discord social conflicts between the components of Iraqi society.
However , the British military administration depended the portioning and deepen the cracks by depending on ethnic as well as religious minorities to achieve its plans in the future and plays on the string of these minorities under the pretext of defending it

By using vacuum evaporation, thin films of the (CdS)0.75-(PbS)0.25 alloy have been deposited to form a nanocrystalline composite. Investigations were made into the morphology, electrical, optical and I-V characteristics of (CdS)0.75-(PbS)0.25 films asdeposited and after annealing at various temperatures. According to AFM measurements, the values of grain sizes rise as annealing temperatures rise, showing that the films' crystallinity has been increased through heat treatment. In addition, heat treatment results in an increase in surface roughness values, suggesting rougher films that could be employed in more applications. The prepared films have direct energy band gaps, and these band gaps increase with the increase in the degrees