In the past I have asked this question by giving the wrong hypothesis.So now I'll try to give the right information. I will be grateful for any help. I have to prove that the following map from $Z/pZ×H$ to $H$ defined as: $(n+pZ)(m/p^i+Z)↦(nm/p^i+Z)$ is well defined (is independent of the choice of representatives). Where $H=G^*[p]$ and $G^*$ is a direct sum of Prüfer groups, so elements in $H$ are elements of $G^*$ such that their order is $p$. thanks
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