On The Linear Group PSL(10, q) Over A Finite Field q = 2^n

The present work will investigate the projective special linear group of dimension 10 over a finite field Fq i.e PSL(10, 2^n)and its maximal subgroups. The main result is a list of maximal subgroups called "the main theorem" which has been proved by using the following well known result "That the minimal normal subgroup of any finite group is either an elementary abelian p-group for some prime number p or a direct product of isomorphic non-abelian simple groups". So, we divided our work into four chapters, the first one "background materials", while chapter two covers, the calculation of the conjugacy classes and the structure of centralizer for the linear group of dimension 10 over a finite field Fq . Chapter three deals with the local analysis for calculating the imprimitive subgroups of G. The fourth chapter deals with the minimal normal subgroups which are the direct product of isomorphic non-Abelian simple groups, this chapter contains three cases: The minimal normal subgroups contains transvections.The minimal normal subgroups does not contain any transvection. The minimal normal subgroups is doubly transitive.