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Homework Help: Abstract Algebra Problem (should be easy)?

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data

    List all the elements of [tex]GL_N(\mathbb{Z}/2\mathbb{Z})[/tex]. Find the order of each element, and show it is not abelian.

    3. The attempt at a solution

    I am confused right from the get go about [tex]GL_n(\mathbb{Z}/2\mathbb{Z})[/tex].

    I think the [tex]L_n(\mathbb{Z}/2\mathbb{Z})[/tex] part means there are a n x n matrices whose elements are [tex]\mathbb{Z}/2\mathbb{Z}[/tex]. Is that correct to say? Also what does the group [tex]G[/tex] have to do in the problem? Any help is appreciated because I am struggling atm to even get started on this problem.
  2. jcsd
  3. Sep 29, 2009 #2
    I don't know much about finite fields but GLn(F) is the "General Linear" Group and is the set of invertible (i.e. non-singular) matrices with components in F.
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