Let G be an abelian group. Show that the set of all elements of G of finite order forms a subgroup of G.?

Ehhh... it's pretty straight-forward...

Let a and b be two elements of finite order in G. We might as well let a^n = b^m = e with n,m > 0.

Show:

(1) a^-1 has finite order. (by the way: o(a^-1) = n)

(2) ab has finite order. (also by the way: o(ab) = lcm(n,m) )

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