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Absract Algebra Problem

  1. Oct 8, 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
    Ok so I know that [tex]\mathbb{Z}/2\mathbb{Z}[/tex] has two elements because [tex]\mathbb{Z}/2\mathbb{Z} = \{ \bar{0}, \bar{1}\}[/tex]. How does the General Linear Group effect the elements of [tex]\mathbb{Z}/2\mathbb{Z}[/tex]? The Genereal Linear Group is defined as: Let F be a field. Then the general linear group [tex]GL_n(F)[/tex] is the group of invertible n x n matrices with entries in F under matrix multiplication.
     
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