here is the question

Determine all the abelian groups A for which the following is true

A tensor B = 0 for every abelian p group B where p is a fixed prime.

I tried to think about this in the language of modules and Z modules first but I didnt get anywhere. Then I tried to think just in group theory terms and I couldnt come up with any finite example. I have an idea that taking infinite products of different p groups for A might work, but no idea how to proceed.