Let $\widetilde G$ and $G$ be Lie groups with identity elements $e_{\widetilde G}$ and $e_G$, respectively. Let $p:\widetilde G\to G$ be a Lie [group homomorphism](/page/Group%20Homomorphism) whose underlying map of topological spaces is a covering map. If $\widetilde G$ is connected, then $\ker p=p^{-1}(\{e_G\})$ is a discrete subgroup of $\widetilde G$ and $\ker p\subset Z(\widetilde G)$.