The Artin' s Exponent of A Special Linear Group SL(2,2k )
Dr.Mohammed Serdar I.Kirdar , Lemia Abd Alameer Hadi
Abstract

The set of all n×n non singular matrices over the field F form a group under the operation of matrix multiplication, This group is called the general linear group of dimension n over the field F, denoted by GL(n,F) . The subgroup from this group is called the special linear group denoted by SL(n,F). We take n=2 and F=2k where k natural, k>1. Thus we have SL (2,2k ). Our work in this thesis is to find the Artin's exponent from the cyclic subgroups of these groups and the character table of it's. Then we have that: a SL(2,2k ) is equal to 2k-1 .
Keywords: Linear Group, Special Group, Exponent.