I have two questions about this group that I think I have an idea about but am unsure of. The first question is how many elements in the Sn group can map 1 to any particular elements, say n-2?
The second question is how do you find the order of the stabilizer of 5 in Sn?
If a and b are in a group, show that if (ab)^n=e then (ba)^n=e.
The Attempt at a Solution
I'm not sure how one would prove this. The question is obviously for non-abelian groups.