Exercise 13, § 4

Let G be a locally compact group and let D be a discrete subgroup of G such that the homogeneous space G/D is compact. Show that, for each $d \in D$, the set of all $sds^{-1}$, as $s$ runs through G, is closed in G. (Prove first, with the help of Proposition 10, that there is a compact subset K of G such that $G = K.D$; then use Corollary 1 to Proposition 1).