Product set growth in Burnside groups

TL;DR

This paper investigates the growth behavior of sub-semi-groups within periodic quotients of torsion-free hyperbolic groups, extending previous results from free groups to a broader class.

Contribution

It provides a detailed lower bound estimate for the growth function of sub-semi-groups in these complex algebraic structures, generalizing earlier work.

Findings

Established a lower growth estimate for sub-semi-groups

Extended Razborov and Safin's results to hyperbolic groups

Enhanced understanding of algebraic growth in group quotients

Abstract

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.