University of Technology-IraqEngineering and Technology Journal1681-6900281020100501The Artin's Exponent of A Special Linear Group SL(2,2k)192419332744910.30684/etj.28.10.5ENMohammedSerdar I.KirdarLemiaAbd Alameer HadiJournal Article20100501The set of all n×n non singular matrices over the field F form a group under<br />the operation of matrix multiplication, This group is called the general linear group<br />of dimension n over the field F, denoted by GL(n,F) .<br />The subgroup from this group is called the special linear group denoted by SL(n,F).<br />We take n=2 and F=2k where k natural, k>1. Thus we have SL (2,2k).<br />Our work in this thesis is to find the Artin's exponent from the cyclic subgroups of<br />these groups and the character table of it's.<br />Then we have that: a SL(2,2k ) is equal to 2k-1 .https://etj.uotechnology.edu.iq/article_27449_d75cf044696fcc78013d1736d2e46aee.pdf