Independence property and hyperbolic groups

TL;DR

This paper demonstrates that existentially closed CSA-groups exhibit the independence property by constructing specific words with this property within torsion-free hyperbolic groups, linking group theory and model theory.

Contribution

It establishes the presence of the independence property in existentially closed CSA-groups through the construction of special words in torsion-free hyperbolic groups.

Findings

Existentially closed CSA-groups have the independence property.

Existence of words with the independence property in torsion-free hyperbolic groups.

Links between model-theoretic properties and hyperbolic group structures.

Abstract

We prove that existentially closed $CSA$-groups have the independence property. This is done by showing that there exist words having the independence property relatively to the class of torsion-free hyperbolic groups.