Equations in Burnside groups

TL;DR

This paper explores equations in periodic groups, focusing on their structure, properties, and automorphisms, with applications to hyperbolic groups' quotients and related algebraic questions.

Contribution

It provides initial insights into equations in periodic groups and analyzes structural properties of their quotients, including automorphisms and free splittings.

Findings

Periodic quotients of hyperbolic groups have specific structural properties.

The study reveals conditions for Hopf and co-Hopf properties in these groups.

Automorphism groups of periodic quotients exhibit particular behaviors.

Abstract

This article is a first step in the study of equations in periodic groups. As an application, we study the structure of periodic quotients of hyperbolic groups. We investigate for instance the Hopf and co-Hopf properties, the isomorphism problem, the existence of free splittings, etc. We also consider the automorphism group of such periodic groups.