# Automorphisms

• March 10th 2009, 09:09 PM
dimuk
Automorphisms
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 $Aut(S_n, S_{n-1})$?
• March 11th 2009, 09:14 AM
InvisibleMan