We consider descending HNN extensions [Formula: see text], where [Formula: see text] is abelian. We show that class-preserving automorphisms of descending HNN extensions are all inner if [Formula: see text] is abelian and [Formula: see text]. It follows that outer automorphism groups of such conjugacy separable descending HNN extensions are residually finite.
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Zhou et al. (2024) studied this question.