1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The orders of GL_2(F_3) and SL_2(F_3)

  1. May 30, 2009 #1
    1. The problem statement, all variables and given/known data
    How to find the orders of [tex]GL_{2}(F_{3}) \, and \, SL_{2}(F_{3})[/tex], where F_3 is the field Z/3Z.


    2. Relevant equations



    3. The attempt at a solution
    I cannot see a proper way to do this, so I just eliminate all those matrices which are not inversible from all 2x2 matrices over F_3. And I got 52 inversible matrices. and the orders of SL(F) should be 26. Since det:GL(F)->{1,2} and considering some properties of ker(det) and the coset.
    I'm not quite confident in my solution, since calculation could be messed up. Is there some better way to solve it?
    Thanks
     
    Last edited: May 30, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: The orders of GL_2(F_3) and SL_2(F_3)
  1. Matrix groups, GL_2(C) (Replies: 8)

  2. First order (Replies: 3)

  3. Reduction of Order (Replies: 2)

  4. Order of this Group (Replies: 29)

Loading...