• THE MAXIMAL SUBGROUPS OF THE UNITARY GROUP PSU (8, q), where q = 2K

Abstract

The purpose of this paper is to study maximal subgroups of the Unitary group PSU (8, q), where q = 2k. The main result is a list of maximal subgroups called "the main theorem" which has been proved by using Aschbacher’s Theorem ([1]). Thus, this work is divided into two main parts:

Part (1): In this part, we will find the maximal subgroups in the classes C1 – C8 of Aschbacher’s Theorem ([1]).

Part (2): In this part, we will find the maximal subgroups in the class C9 of Aschbacher’s Theorem ([1]), which are the maximal primitive subgroups H of G that have the property that the minimal normal subgroup M of H is not abelian group and simple, thus, we divided this part into two cases:

Case (1): M is generated by transvections: In this case, we will use result of Kantor ([9]).

Case (2): M is a finite primitive subgroup of rank three: In this case, we will use the classification of Kantor and Liebler ([8]).