Let ${{G}_{1}}$ and ${{G}_{2}}$ be $p$-adic groups. We describe a decomposition of Ext-groups in the category of smooth representations of ${{G}_{1}}\times {{G}_{2}}$ in terms of Ext-groups for ${{G}_{1}}$ and ${{G}_{2}}$. We comment on $\text{Ext}_{G}^{1}\left( \pi ,\pi \right)$ for a supercuspidal representation $\pi$ of a $p$-adic group $G$. We also consider an example of identifying the class, in a suitable $E\text{x}{{\text{t}}^{1}}$, of a Jacquet module of certain representations of $p$-adic $\text{G}{{\text{L}}_{2n}}$.