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?
Yes, as in having an infinite number of elements. What if we wanted a group with order infinity that had a relatively small number of elements of finite order?
I'm not sure how this helps us show that (ba)^2=e? When generalizing to (ab)^n I see we'll get a similar result but I'm not sure how this shows that (ba)^n=e.
Homework Statement
If a and b are in a group, show that if (ab)^n=e then (ba)^n=e.
Homework Equations
The Attempt at a Solution
I'm not sure how one would prove this. The question is obviously for non-abelian groups.