Uniform symplicity of groups with proximal action

TL;DR

This paper demonstrates that certain groups with highly dynamic actions on linear orders or Cantor sets are uniformly simple, providing explicit bounds and including notable classes like Higman-Thomson and Neretin groups.

Contribution

It establishes uniform simplicity for groups with specific proximal actions, extending understanding of their algebraic structure and providing explicit bounds.

Findings

Groups with bounded, order-primitive actions are uniformly simple.

Includes Higman-Thomson and Neretin groups as special cases.

Provides explicit bounds for simplicity.

Abstract

We prove that groups acting boundedly and order-primitively on linear orders or acting extremly proximality on a Cantor set (the class including various Higman-Thomson groups and Neretin groups of almost automorphisms of regular trees, also called groups of spheromorphisms) are uniformly simple. Explicit bounds are provided.