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.

تستهدف هذه الدراسة وبشكل أساس، الكشف عن طبيعة وخصائص البعد السياسي لهندسة/صناعة الخصائص الاجتماعية والسياسية للإنسان والمجتمع، بوصفها العملية المسؤولة عن تصميم هذه الخصائص وصناعتها وتغييرها جزئيا أو كليا، دون أبعادها الأخرى المتعددة والمتنوعة، لا لمجرد الانسياق وراء دوافع الرغبة الذاتية، أو اعتبارات التخصص الدقيق وأحكامه، لأن معهما أيضا، بل وقبلهما أحيانا، دوافع واعتبارات أخرى موضوع

The research studies the sculptural formation in the third millennium: styles and trends, by taking the most important results of sculpture in the third millennium. The problem of the research is to search for the new sculptural formation in what it constitutes of social and human importance, and what are the important factors in forming the   contemporary sculptural structure, and what is the mechanism of showing and producing the new formation. The research requires the study of the most important thing that the (sculptural formation in the third millennium styles and trends) represents. The importance of research depends on the importance of the sculptural formation after the twentieth century and the importance that the for

Contrary to deconstruction and its destructive pursuit, the concept of undermining the familiar seeks to refute the constants and its known limitations. It is done through the process of receiving and what is imposed by the formation of the word or text or the structural and design structure in general, along with the Arabic calligraphy in particular. This is based on the recipient's understanding and interpretation of the dual phenomenon and the content's manifestation. More accurately, the disclosure of its reality through its expressive phenomenology; for that sake, the research was devoted to studying “undermining the familiar and embodiment content in Arabic calligraphy” including four chapters. The first chapter comprised

     Let  be a ring with identity. Recall that a submodule  of a left -module  is called strongly essential if for any nonzero subset  of , there is  such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule  of  is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module  is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of  is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules  and  of  that a module  has the

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.

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.