Q: If $ H = \{ \sigma \in S_n : \sigma(n) = n \} $ is a subgroup of $S_n$, then show that $H \simeq S_{n-1}$.
I know any group is isomorphic to a subgroup of the symmetric group. But I don't know how to proceed.
Q: If $ H = \{ \sigma \in S_n : \sigma(n) = n \} $ is a subgroup of $S_n$, then show that $H \simeq S_{n-1}$.
I know any group is isomorphic to a subgroup of the symmetric group. But I don't know how to proceed.