For each , let be the set of all permutations in which fix r. Then is a set of permutations on n-1 numbers, so - hence , and there is a one-to-one correspondence between and
Last edited by Catherine Morland; August 6th 2008 at 12:16 PM.
Here is a similar question I was thinking of.
Find all the index n subgroups of S_n.
Is it S(1), ... S(n) - where S(i) are permutations which fix i?
I know this is true for n=3,4.
But how do we prove it if it is true?