Let G be an abelian group and let g,h Є G.
(i) Assuming that |g| and |h| are both finite, with hcf (|g| , |h|) = 1. Prove that
|g + h| = |g| |h|
(ii) prove that the direct sum of Zm and Zn is isomorphic to Zmn if and only if m and n are relatively prime.
any help would be appreciated. thanks