Bounded automorphisms of groups
Let \(G\) be the fundamental group of a graph of groups (in the sense of Bass-Serre theory). Such a group has a natural length function and thus a corresponding notion of bounded subgroups and bounded automorphisms. The general result of this paper is that an automorphism of \(G\) is bounded if and only if it is induced by isomorphisms of vertex groups and inner automorphisms. In the special cases that \(G\) is an HNN-extension or an amalgamated free product \(G_ 1 *_{G_ 0} G_ 2\), more specific characterizations of bounded automorphisms are obtained. If moreover \(G_ 1\) and \(G_ 2\) are groups of type (FA), then a presentation of \(\text{Aut}(G)\) is given in terms of \(\text{Aut}(G_ i)\) \((i = 0,1,2)\). All proofs, most of which are rather elementary considerations in Bass- Serre theory, are given in full detail.
scientific article; zbMATH DE number 645114