LetGbe an abelian group and letg,hЄG.

(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