  This paper presents a study of generic elements in full isometry groups of
Polish ultrametric spaces. We obtain a complete characterization of Polish
ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H
with ample generics. It also gives a characterization of the existence of an
open subgroup in Iso(X) with a comeager conjugacy class.
  We also study the transfinite sequence defined by the projection of a Polish
ultrametric space X on the ultrametric space of orbits of X under the action of
Iso(X).

Group Theory