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Let $ G$ be locally compact group, and $ H$ be a subgroup of the center of $ G$ . Is there a continuous homomorphism $ \phi: G \to \mathbb{Q}/\mathbb{Z}$ such that $ H \not\subset \ker \phi$ ? Or, more generally, given a continuous homomorphism $ \gamma: H \to \mathbb{Q}/\mathbb{Z}$ , can we extend $Read more