On Certain 3-Transposition Groups in Exceptional Groups Over Fields K of Characteristic Two

يهدف هذا المشروع الى بناء الاحتواء 3.F_i22≤3.E_6 (2)≤3.E_6 (4)≤GL(27,4) بإسلوب شفاف وبسيط باستخدام مجموعة M وكذلك بعض تقنيات الجبر الخطي ونأمل كذلك من اثبات وجود F_i22 واثبات انها محتواه في 〖2U〗_6(2).

The purpose of this project is to construct an explicit embedding 3.〖 F〗_i22≤3.E_6 (2)≤3.E_6 (4)≤GL(27,4)in an elementary and transparent fashion based on the notion of M-sets, We hope to show the existence of F_i22 and from the existence proof one can investigate whether F_i22 can be embedded in 〖2U〗_6(2). The approach we follow is elementary and transparent on the account that it consists of little more than naïve linear algebra.