A sample iterated small cancellation theory for groups of Burnside type

TL;DR

This paper introduces a new method to present free Burnside groups of odd exponent using iterated small cancellation conditions, providing an accessible proof of their infiniteness for exponents greater than 2000.

Contribution

It develops a novel technique for representing Burnside groups with small cancellation conditions and offers a simplified proof of their infiniteness for large odd exponents.

Findings

Proves that free Burnside groups are infinite for odd exponents n > 2000.

Introduces an iterated small cancellation approach for Burnside groups.

Provides an accessible proof compared to previous complex methods.

Abstract

We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.