Isometry types of profinite groups

TL;DR

This paper investigates the structure of closed subgroups of the isometry group of a rooted tree using model-theoretic methods, focusing on conjugacy class properties.

Contribution

It introduces a novel approach to analyze subgroup conjugacy classes in isometry groups of rooted trees through model theory.

Findings

Characterization of conjugacy class distributions in subgroups

Application of model-theoretic techniques to group actions

Insights into the structure of isometry groups of rooted trees

Abstract

Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.