The Artin's Exponent of A Special Linear Group SL(2,2k)
Engineering and Technology Journal,
2010, Volume 28, Issue 10, Pages 1924-1933
AbstractThe 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 .
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