Automorphisms

**dimuk** · March 10th 2009, 09:09 PM

How to find the $Aut(S_n, S_{n-1})$ ?

I know this is equal to $\frac{N_{Aut(S_n)}(S_{n-1})}{C_{Aut(S_n)}(S_{n-1})}$ for all n.

Since $Aut(S_n)=S_n$ unless $n \not= 6$ , $Aut(S_n, S_{n-1})=\frac{N_{S_n}(S_{n-1})}{C_{S_n}(S_{n-1})}$ when $n\not = 6$ .

When $n=6, Out(S_6)=\frac{Aut(S_6)}{Inn(S_6)}$ .
What is happening when $n=6$ for $Aut(S_n, S_{n-1})$ ?

**InvisibleMan** · March 11th 2009, 09:14 AM

I don't understand your notation.
For example what Aut(X,Y) means, I mean Aut(X) means the set of all automorphisms on X.

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