In the proof of the the lemma
suppose $G$ is a finite abelian $p$-group, and let $C$ a cyclic subgroup of maximal order, then $G=C\oplus H$ for some subgroup $H$
at http://torus.math.uiuc.edu/jms/m317/handouts/finabel.pdf,
They say that since $H\cap(C+K)= K$, we have $H\cap C=\{e\}$. But how do they have that $H\cap(C+K)= K$? Can someone prove that please is because I don't see why is that true with the arguments presented in that proof. thanks a lot in advance :)
I am sorry for this but my doubt was in the part that I pst here and in the other question the answer was to other thing :)