University of Technology-IraqEngineering and Technology Journal1681-6900281020100528The Artin's Exponent of A Special Linear Group SL(2,2k)اس ارتن للزمر الخطية الخاصة (SL(2,2K1924193327449ENMohammed Serdar I.KirdarLemia Abd Alameer HadiJournal Article20100501The 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 .https://etj.uotechnology.edu.iq/article_27449_8a5f456b95e19561fad1e4747eea11c0.pdf