Small cancellation theory and Burnside problem

TL;DR

This paper discusses the application of small cancellation theory, a geometric approach, to prove the infiniteness of certain algebraic groups like free Burnside groups and hyperbolic groups with torsion-free properties.

Contribution

It provides a new geometric proof of the infiniteness of free Burnside groups and periodic quotients of torsion-free hyperbolic groups using small cancellation theory.

Findings

Proves the infiniteness of free Burnside groups.

Establishes periodic quotients of torsion-free hyperbolic groups.

Utilizes a geometric approach to group theory.

Abstract

In these notes we detail the geometrical approach of small cancellation theory used by T. Delzant and M. Gromov to provide a new proof of the infiniteness of free Burnside groups and periodic quotients of torsion-free hyperbolic groups.