Given a group is abelian, o(x) and o(y) are finite, show o(x*y) is finite.
Does anyone have any ideas on this one that could help get me started?
Here is about as far as I've come so far.
there are integers m, n such that x^m = e and y^n = e
x*y = y*x
we want to show:
there is an integer j where (x*y)^j = e
the question also wants me to show that that o(xy) divides o(x)*o(y). I'm thinking that the fact that i'm going to be able to show:
there is an integer a where j * a = m * n
is going to be helpful with the first question, but i haven't figured out how yet