Proper decompositions of finitely presented groups

TL;DR

This paper discusses a long-term research project aimed at developing an algorithm to determine whether finitely presented groups can act non-trivially on trees, contributing to understanding their structural properties.

Contribution

It introduces a new approach to decide if finitely presented groups admit non-trivial actions on trees, advancing the computational methods in geometric group theory.

Findings

Proposed an algorithmic framework for group actions on trees

Established criteria for non-trivial actions on trees

Progressed towards an effective decision procedure

Abstract

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.