Abstract
Abstract The paper is devoted to a study of isometry groups of Polish ultrametric spaces. We explicitly describe isometry groups of spaces that are non-locally rigid and satisfy the property that distances between orbits under the action of the isometry group are realized by points. The type of group construction appearing here is a variant of the generalized wreath product. We prove that it has a natural universality and uniqueness property. As an application, we characterize Polish ultrametric spaces satisfying the above properties, whose isometry groups have uncountable strong cofinality.
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