On the automorphisms of the fundamental group of a graph of groups and their fixed points

Let G be the fundamental group of a graph of groups and X the corresponding universal tree. We consider the extension of the action of G on X to an action of the subgroup of automorphisms of G which map vertex groups onto conjugates of, themselve.4nd obtain a structure theorem for this subgroup. We also prove results that cad be used to give bounds for the complexity of the graph of groups decomposition of the fixed subgroups of these automorphisms. 2000 Mathematics Subject Classification: 20F28, 20E06, 20E08.