10.33 (1986)

For HNN-extensions of the form $G = \langle t, A \mid t^{-1}Bt = C, \phi \rangle$, where $A$ is a finitely generated abelian group and $\phi : B \to C$ is an isomorphism of two of its subgroups, find
$\qquad$ a) a criterion to be residually finite;
$\qquad$ b) a criterion to be Hopfian.