Let H= {phi element of Sn | phi(n)=n}
What's the index of H in Sn?
the index of H in Sn = |Sn|/|H|
and I know |Sn|= n!
I was told the order of H is (n-1)! but i don't see how
Could anyone help?
Basically $\displaystyle H$ are all permutations that fix $\displaystyle n$. Therefore $\displaystyle H$ can be regarded as the group of all permutations of $\displaystyle \{ 1,2,...n-1\}$ i.e. isomorphic to $\displaystyle S_{n-1}$ and so $\displaystyle |H| = (n-1)!$.