Let $G$ be a locally compact topological group, $K$ a compact subgroup and $\Gamma$ a discrete subgroup. I try to find a neighbourhood $U$ of the identity such that $\Gamma \cap UK = \Gamma \cap K$. How can I construct such a neighbourhood? If $K$ is trivial, the existence of $U$ follows from the discreteness of $\Gamma$.
Do you have some good references on topological groups?