Paradoxical decomposition of Group Actions and Configuration

TL;DR

This paper explores the concept of configuration in group actions, extending properties known for groups to actions, and investigates their connection with the ping-pong lemma, revealing new insights into group dynamics.

Contribution

It introduces the notion of configuration for group actions and extends existing properties, linking them with the ping-pong lemma for the first time.

Findings

Properties of configurations extend from groups to actions

Connection established between configuration and ping-pong lemma

New insights into group action dynamics

Abstract

In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different types of well-known ping-pong lemma is also investigated.