  We prove that every reflexive abelian group $G$ such that its dual group
$G^\wedge$ has the $qc$-Glicksberg property is a Mackey group. We show that a
reflexive abelian group of finite exponent is a Mackey group. We prove that,
for a realcompact space $X$, the space $C_k(X)$ is barrelled if and only if it
is a Mackey group.
