I want to show that:
If $G=\prod_{p\in P}\mathbb Z_p$, wherein $P$ is the set of all primes, then $\frac{G}{tG}$ is divisible.
I know that $tG$ is not a direct summand and if $x\in G$ wants to be divisible by every primes, it will be $0$. I wanted to know $tG$ for myself first, so I took an element in it: $f=(a_1,a_2,...)\in tG\longrightarrow\exists n, nf=0 $ Can I conclude here that for infinitely many $a_i\in \mathbb Z_{p_i}$, we necessarily have $a_i=0$? Is there any formal well-known description for $tG$? Thanks for any hint or references of where to start the main problem above.