A follow up to a previous question of mine.
I thought it was true, but according to my book $G \simeq H \oplus K$, with $G \simeq H$ does not imply $K=0$
Is there a simple counter example? In what situation is this true?
(Motivation is, from the previous question, to show that $H_n(X,A)=0$
Edit: The groups are Abelian