Bulletin of the
Korean Mathematical Society BKMS

We show that, for any non-zero integers $\la$, $\mu$, $\nu$, $\xi$, class-preserving automorphisms of the group $$G(\la, \mu, \nu, \xi) =\cy{a,b,t: b^{-1} a^{\la} b=a^{\mu}, t^{-1} a^\nu t = b^\xi }$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G(\la, \pm\la, \nu, \xi)$ is residually finite.

Keywords: HNN extensions, residually finite, conjugacy separable, Baumslag-Solitar groups

MSC numbers: Primary 20E26, 20E06; Secondary 20F10