The title is the question. Is $A_n$ characteristic in $S_n$?
If $\phi \in \operatorname{Aut}(S_n)$, Then $[S_n : \phi(A_n)]$ (The index of $\phi(A_n)$) is 2. Maybe the only subgroup of $S_n$ of index 2 is $A_n$?
Thanks in advance.
The title is the question. Is $A_n$ characteristic in $S_n$?
If $\phi \in \operatorname{Aut}(S_n)$, Then $[S_n : \phi(A_n)]$ (The index of $\phi(A_n)$) is 2. Maybe the only subgroup of $S_n$ of index 2 is $A_n$?
Thanks in advance.