[For the entire collection see Zbl 0652.00004.]
Let G be a group, \(G_{ab}\) the abelianization \(G/G'\) of G and \(\pi_{ab}: Aut G\to Aut G_{ab}\) the canonical homomorphism in which each automorphism of G is mapped onto the automorphism it induces on \(G_{ab}\). The kernel of \(\pi_{ab}\) (denoted by IA(G)) is the group of IA-automorphisms of G. In a recent paper [J. Lond. Math. Soc., II. Ser. 36, No.3, 393-406 (1987; Zbl 0638.20022)] S. Bachmuth, G. Baumslag, J. Dyer and H. Mochizuki investigated the group IA(G) for G a 2-generator metabelian group and proved that Aut G is finitely generated if and only if IA(G) is. The present note suggests similar methods for the study of automorphism groups of more complicated groups such as finitely generated abelian-by-nilpotent groups. The focal point is the quest for analogues to the stabilizer results of D. Farkas and R. Snider [Invent. Math. 75, 75-82 (1984; Zbl 0532.16006)]. There are many technical details and 23 references.