Conditions for size of index

  • Thread starter epkid08
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  • #1
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Main Question or Discussion Point

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}
\end{cases}[/tex]

Basically I want to know what the conditions are.

Note that [tex]C[/tex] is the centralizer.
 

Answers and Replies

  • #2
263
1
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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