Corollary 1

— If G is a commutative group annihilated by n, and $G \neq \{1\}$, then $\mathrm{Hom}(G, T) \neq \{1\}$.

For it suffices to note that if H is a cyclic subgroup of G distinct from $\{1\}$, then $\mathrm{Hom}(H, T) \neq \{1\}$, and to apply Prop. 7.