Class-preserving automorphisms of certain HNN extensions

We show that, for any integers γ,βγ,β, class-preserving automorphisms of the HNN extension 〈B,t:t−1hγt=hβ〉〈B,t:t−1hγt=hβ〉 of a finitely generated nilpotent or free group B are all inner. It follows from Grossman's result that outer automorphism groups of such conjugacy separable HNN extensions are residually finite.