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Conditions for size of index

  1. Oct 22, 2013 #1
    For any element [tex]x \in A_5[/tex], we have that [tex][A_5:C_{A_5}(x)]=\begin{cases}
    [S_5:C_{S_5}(x)], & \text{condition 1} \\
    \frac{1}{2}[S_5:C_{S_5}(x)], & \text{condition 2}

    Basically I want to know what the conditions are.

    Note that [tex]C[/tex] is the centralizer.
  2. jcsd
  3. Oct 22, 2013 #2
    I'm just talking to myself here, but I think condition 1 is "[tex]x[/tex] takes the form [tex](abc)[/tex]" and condition 2 is "[tex]x[/tex] takes the form [tex](abcde)[/tex]."

    Anybody want to verify?
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