bilinear map of abelian groups

Let \(G_1,G_2,G_3\) be abelian groups. A bilinear map

\begin{align*} \varphi: G_1 \times G_3 \rightarrow G_3 \end{align*}

is a bilinear map of \(\mathbb{Z}\)-modules

see: abelian group as module over the integers