The Artin's Exponent of A Special Linear Group SL(2,2k)
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Unviversity of Technology- Iraq
2010-05-01
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| Series: | Engineering and Technology Journal |
| Subjects: | |
| Online Access: | https://etj.uotechnology.edu.iq/article_27449_d75cf044696fcc78013d1736d2e46aee.pdf |
| Summary: | 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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| ISSN: | 1681-6900 2412-0758 |