Title: A locally quasi-convex abelian group without Mackey topology,
Abstract: We give the first example of a locally quasi-convex (even countable reflexive
and $k_\omega$) abelian group $G$ which does not admit the strongest compatible
locally quasi-convex group topology. Our group $G$ is the Graev free abelian
group $A_G(\mathbf{s})$ over a convergent sequence $\mathbf{s}$.