### The Artin's Exponent of A Special Linear Group SL(2,2k)

*Engineering and Technology Journal*

2010, Volume 28, Issue 10, Pages 1924-1933

2010, Volume 28, Issue 10, Pages 1924-1933

#### Abstract

The set of all n×n non singular matrices over the field F form a group underthe operation of matrix multiplication, This group is called the general linear groupof 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 ofthese 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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