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Thread: Automorphisms

  1. #1
    Junior Member
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    Jul 2008
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    54

    Automorphisms

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

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


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

    When $\displaystyle n=6, Out(S_6)=\frac{Aut(S_6)}{Inn(S_6)}$.
    What is happening when $\displaystyle n=6$ for $\displaystyle Aut(S_n, S_{n-1})$?
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  2. #2
    Junior Member
    Joined
    Jan 2009
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    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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